design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

fully implicit methodology for the dynamics of biomembranes and capillary interfaces by combining the level set and newton methods abstract this framework is concerned with the numerical modeling of the dynamics of individual biomembranes and capillary interfaces in a surrounding newtonian fluid a level set approach helps to follow the interface motion our method features the use of high order fully implicit time integration schemes that enable to overcome stability issues related to the explicit discretization of the highly non linear bending force or capillary force at each time step the tangent systems are derived and the resulting nonlinear problems are solved by a newton raphson method based on the signed distance assumption several inexact newton strategies are employed to solve the capillary and vesicle problems and guarantee the second order convergence behavior we address in detail the main features of the proposed method and we report several experiments in the two dimensional case with the aim of illustrating its accuracy and efficiency comparative investigations with respect to the fully explicit scheme depict the stabilizing effect of the new method which allows to use significantly larger time step sizes

three dimensional volume conserving immersed boundary model for two phase fluid flows abstract we present a volume preserving scheme for two phase immiscible incompressible flows using an immersed boundary method ibm in a three dimensional space the two phase ibm employs a mixture of eulerian and lagrangian variables where the fluid interface is represented by discrete lagrangian markers exerting surface tension forces to the eulerian fluid domain and the markers are advected by the fluid velocity the interactions between the lagrangian markers and the fluid variables are linked by the discretized dirac delta function the present study extends the previous two dimensional research li et al volume preserving immersed boundary methods for two phase fluid flows int j numer meth fluids 69 2012 842 858 to the three dimensional space the key idea of the proposed method is relocating surface points along the normal directions to conserve the total volume we perform a number of numerical experiments to show the efficiency and accuracy of the proposed method

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

efficient pseudospectral flow simulations in moderately complex geometries a computationally efficient pseudospectral method is developed for incompressible flow simulations in two dimensional geometries involving periodicity in one direction and significant surface deformations a pseudoconformal mapping is used to map the flow domain into a rectangle thereby establishing an orthogonal curvilinear coordinate system within which the governing equations are formulated the time integration of the spectrally discretized two dimensional momentum equations is performed by a second order mixed explicit implicit time integration scheme the satisfaction of the continuity equation is obtained through the solution of a poisson equation for the pressure and the use of the influence matrix technique a highly efficient iterative solver has been developed for the solution of a generalized stokes problem at each time step based on a spectrally preconditioned biconjugate gradient algorithm which exhibits almost linear scalability requiring an ordernlog2nnumber of operations wherenis the number of unknowns numerical results are presented for two dimensional steady oscillatory and peristaltic flows within an undulating channel which agree well with previous results that have appeared in the literature

uniform preconditioners for a parameter dependent saddle point problem with application to generalized stokes interface equations we consider an abstract parameter dependent saddle point problem and present a general framework for analyzing robust schur complement preconditioners the abstract analysis is applied to a generalized stokes problem which yields robustness of the cahouet chabard preconditioner motivated by models for two phase incompressible flows we consider a generalized stokes interface problem application of the general theory results in a new schur complement preconditioner for this class of problems the robustness of this preconditioner with respect to several parameters is treated results of numerical experiments are given that illustrate robustness properties of the preconditioner

a quadratic spline based interface quasi reconstruction algorithm for accurate tracking of two phase flows a new quadratic spline based interface quasi reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature the fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous plic approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves the conversion is achieved by a sequence of predictor corrector operations enforcing function c 0 and derivative c 1 continuity at the cell boundaries using simple analytical expressions for the continuity requirements the efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations these benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes only in situations where the interface geometry is primarily flat the rate of convergence becomes linear with the mesh size the flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location as a consequence it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface this has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium finally the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water

simulation of surface tension in 2d and 3d with smoothed particle hydrodynamics method the methods for simulating surface tension with smoothed particle hydrodynamics sph method in two dimensions and three dimensions are developed in 2d surface tension model the sph particle on the boundary in 2d is detected dynamically according to the algorithm developed by dilts g a dilts moving least squares particle hydrodynamics ii conservation and boundaries international journal for numerical methods in engineering 48 2000 1503 1524 the boundary curve in 2d is reconstructed locally with lagrangian interpolation polynomial in 3d surface tension model the sph particle on the boundary in 3d is detected dynamically according to the algorithm developed by haque and dilts a haque g a dilts three dimensional boundary detection for particle methods journal of computational physics 226 2007 1710 1730 the boundary surface in 3d is reconstructed locally with moving least squares mls method by transforming the coordinate system it is guaranteed that the interface function is one valued in the local coordinate system the normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated surface tension force acts only on the boundary particle density correction is applied to the boundary particle in order to remove the boundary inconsistency the surface tension models in 2d and 3d have been applied to benchmark tests for surface tension the ability of the current method applying to the simulation of surface tension in 2d and 3d is proved

simulation of axisymmetric jets with a finite element navier stokes solver and a multilevel vof approach a multilevel vof approach has been coupled to an accurate finite element navier stokes solver in axisymmetric geometry for the simulation of incompressible liquid jets with high density ratios the representation of the color function over a fine grid has been introduced to reduce the discontinuity of the interface at the cell boundary in the refined grid the automatic breakup and coalescence occur at a spatial scale much smaller than the coarse grid spacing to reduce memory requirements we have implemented on the fine grid a compact storage scheme which memorizes the color function data only in the mixed cells the capillary force is computed by using the laplace beltrami operator and a volumetric approach for the two principal curvatures several simulations of axisymmetric jets have been performed to show the accuracy and robustness of the proposed scheme

mean value identities as an opportunity for monte carlo error reduction in the monte carlo simulation of both lattice field theories and of models of statistical mechanics identities verified by exact mean values such as schwinger dyson equations guerra relations callen identities etc provide well known and sensitive tests of thermalization bias as well as checks of pseudo random number generators we point out that they can be further exploited as control variates to reduce statistical errors the strategy is general very simple and almost costless in cpu time the method is demonstrated in the two dimensional ising model at criticality where the cpu gain factor lies between 2 and 4

cross correlations in scaling analyses of phase transitions thermal or finite size scaling analyses of importance sampling monte carlo computer simulations in the vicinity of phase transition points often combine different estimates for the same quantity such as a critical exponent with the intent to reduce statistical fluctuations we point out that the origin of such estimates in the same time series often results in pronounced cross correlations which are usually ignored even in high precision studies generically leading to significant underestimation of statistical fluctuations we suggest to use a simple extension of the conventional analysis taking correlation effects into account which leads to improved estimators with often substantially reduced statistical fluctuations at almost no extra cost in terms of computation time

a new approach to sub grid surface tension for les of two phase flows in two phase flow the presence of inter phasal surface the interface causes additional terms to appear in les formulation those terms were ignored in contemporary works for the lack of model and because the authors expected them to be of negligible influence however it has been recently shown by a priori dns simulations that the negligibility assumption can be challenged in the present work a model for one of the sub grid two phase specific terms is proposed using deconvolution of the velocity field and advection of the interface using that field using the model the term can be included into les a brief presentation of the model is followed by numerical tests that assess the model s performance by comparison with a priori dns results

monte carlo simulation with fluctuating boundary conditions abstract i study the finite size behavior of the ratio of partition functions with periodic and antiperiodic boundary conditions in the vicinity of the critical coupling of the 3d ising model this ratio is obtained as a simple expectation value in an ensemble where i average over both kinds of boundary conditions based on such simulations i obtain c 0 221650 5 and 0 630 2 these results are compared with fourth order cumulant results obtained in the same monte carlo simulations

smoothed particle hydrodynamics continuous boundary force method for navier stokes equations subject to a robin boundary condition a robin boundary condition for the navier stokes equations is used to model slip conditions at the fluid solid boundaries a novel continuous boundary force cbf method is proposed for solving the navier stokes equations subject to the robin boundary condition in the cbf method the robin boundary condition is replaced by the homogeneous neumann boundary condition and a volumetric force term added to the momentum conservation equation smoothed particle hydrodynamics sph method is used to solve the resulting navier stokes equations we present solutions for two and three dimensional flows subject to various forms of the robin boundary condition in domains bounded by flat and curved boundaries the numerical accuracy and convergence are examined through comparison of the sph cbf results with the solutions of finite difference or finite element method considering the no slip boundary condition as a special case of the slip boundary condition we demonstrate that the sph cbf method accurately describes both the no slip and slip conditions

new performance bounds for turbo codes we derive a new upper bound on the word and bit error probabilities of turbo codes with maximum likelihood decoding by using the gallager bound since the derivation of the bound for a given interleaver is intractable we assume uniform interleaving as in the derivation of the standard union bound for turbo codes the result is a generalization of the transfer function bound and remains useful for a wider range of signal to noise ratios particularly for some range below the channel cutoff rate the new bound is also applicable to other linear codes

on ensembles of low density parity check codes asymptotic distance distributions we derive expressions for the average distance distributions in several ensembles of regular low density parity check codes ldpc among these ensembles are the standard one defined by matrices having given column and row sums ensembles defined by matrices with given column sums or given row sums and an ensemble defined by bipartite graphs

evolution implementation and application of level set and fast marching methods for advancing fronts abstract a variety of numerical techniques are available for tracking moving interfaces in this review we concentrate on techniques that result from the link between the partial differential equations that describe moving interfaces and numerical schemes designed for approximating the solutions to hyperbolic conservation laws this link gives rise to computational techniques for tracking moving interfaces in two and three space dimensions under complex speed laws we discuss the evolution of these techniques the fundamental numerical approximations involved implementation details and applications in particular we review some work on three aspects of materials sciences semiconductor process simulations seismic processing and optimal structural topology design

incompressible smoothed particle hydrodynamics for free surface flows a generalised diffusion based algorithm for stability and validations for impulsive flows and propagating waves the incompressible smoothed particle hydrodynamics isph method with projection based pressure correction has been shown to be highly accurate and stable for internal flows and importantly for many problems the pressure field is virtually noise free in contrast to the weakly compressible sph approach xu et al 2009 31 however for almost inviscid fluids instabilities at the free surface occur due to errors associated with the truncated kernels a new algorithm is presented which remedies this issue giving stable and accurate solutions to both internal and free surface flows generalising the particle shifting approach of xu et al 2009 31 the algorithm is based upon fick s law of diffusion and shifts particles in a manner that prevents highly anisotropic distributions and the onset of numerical instability the algorithm is validated against analytical solutions for an internal flow at higher reynolds numbers than previously the flow due to an impulsively started plate and highly accurate solutions for wet bed dam break problems at zero and small times the method is then validated for progressive regular waves with paddle motion defined by linear theory the accurate predictions demonstrate the effectiveness of the algorithm in stabilising solutions and minimising the surface instabilities generated by the inevitable errors associated with truncated kernels the test cases are thought to provide a more thorough quantitative validation than previously undertaken

a front tracking front capturing method for the simulation of 3d multi fluid flows with free surfaces a method for simulating incompressible imiscible unsteady newtonian multi fluid flows with free surfaces is described a sharp interface separates fluids of different density and viscosity surface and interfacial tensions are also considered and the required curvature is geometrically approximated at the fronts by a least squares quadratic fitting to remove small undulations at the fronts a mass conserving filter is employed the numerical method employed to solve the navier stokes equations is based on the gensmac 3d front tracking method the velocity field is computed using a finite difference scheme on an eulerian grid the free surface and the interfaces are represented by an unstructured lagrangian grid moving through an eulerian grid the method was validated by comparing the numerical results with analytical results for a number of simple problems complex numerical simulations show the capability and emphasize the robustness of this new method

a free energy based surface tension force model for simulation of multiphase flows by level set method in this paper a free energy based surface tension force fesf model is presented for accurately resolving the surface tension force in numerical simulation of multiphase flows by the level set method by using the analytical form of order parameter along the normal direction to the interface in the phase field method and the free energy principle fesf model offers an explicit and analytical formulation for the surface tension force the only variable in this formulation is the normal distance to the interface which can be substituted by the distance function solved by the level set method on one hand as compared to conventional continuum surface force csf model in the level set method fesf model introduces no regularized delta function due to which it suffers less from numerical diffusions and performs better in mass conservation on the other hand as compared to the phase field surface tension force pfsf model the evaluation of surface tension force in fesf model is based on an analytical approach rather than numerical approximations of spatial derivatives therefore better numerical stability and higher accuracy can be expected various numerical examples are tested to validate the robustness of the proposed fesf model it turns out that fesf model performs better than csf model and pfsf model in terms of accuracy stability convergence speed and mass conservation it is also shown in numerical tests that fesf model can effectively simulate problems with high density viscosity ratio high reynolds number and severe topological interfacial changes a free energy based surface tension force fesf model is proposed for simulation of multiphase flows by level set method the proposed model computes the surface tension force by an explicit form the proposed model outperforms the existing models in terms of accuracy stability convergence speed and mass conservation the proposed model can effectively simulate multiphase flows

an accurate adaptive solver for surface tension driven interfacial flows a method combining an adaptive quad octree spatial discretisation geometrical volume of fluid interface representation balanced force continuum surface force surface tension formulation and height function curvature estimation is presented the extension of these methods to the quad octree discretisation allows adaptive variable resolution along the interface and is described in detail the method is shown to recover exact equilibrium to machine accuracy between surface tension and pressure gradient in the case of a stationary droplet irrespective of viscosity and spatial resolution accurate solutions are obtained for the classical test case of capillary wave oscillations an application to the capillary breakup of a jet of water in air further illustrates the accuracy and efficiency of the method the source code of the implementation is freely available as part of the gerris flow solver

an accurate low mach scheme for a compressible two fluid model applied to free surface flows classical approximate riemann solvers are known to be too much dissipative in the low mach number regime for this reason since the mach number in liquids is generally very small usual upwind schemes may provide inaccurate solutions when applied to the simulation of two phase flows in this paper to circumvent this difficulty while keeping a compressible model for the description of both gas and liquid an original accurate low mach scheme is introduced and theoretically studied extending some ideas already used for the gas dynamics system the proposed scheme is based on a centred formulation for the pressure gradient term in the momentum equation and on the introduction of a stabilising term proportional to the pressure difference between two neighbouring cells the scheme stability is ensured and theoretically proved under a convective cfl like condition by using a semi implicit time discretisation algorithm finally the correct asymptotic behaviour of the scheme in the limit of small mach numbers is assessed on several academic test cases

bounds on the decoding error probability of binary linear codes via their spectra bounds on the error probability of maximum likelihood decoding of a binary linear code are considered the bounds derived use the weight spectrum of the code and they are tighter than the conventional union bound in the case of large noise in the channel the bounds derived are applied to a code with an average spectrum and the result is compared to the random coding exponent the author shows that the bound considered for the binary symmetrical channel case coincides asymptotically with the random coding bound for the case of awgn channel the author shows that berlekamp s 1980 tangential bound can be improved but even this improved bound does not coincide with the random coding bound although it can be very close to it

arbitrary lagrangian eulerian finite element analysis of free surface flow an arbitrary lagrangian eulerian ale description of newtonian fluid flow is presented it allows the simulation of free surfaces with the finite element method fem we develop a robust node repositioning algorithm which consists of two parts an energy minimization principle controls the positions of the internal nodes a good approximation of the boundaries is ensured by explicitly enforcing the free surface conditions numerical examples are done employing the mini element

efficient implementation of thinc scheme in this paper we improve the multi dimensional thinc tangent of hyperbola for interface capturing scheme f xiao y honma t kono a simple algebraic interface capturing scheme using hyperbolic tangent function int j numer meth fluid 48 2005 1023 the thinc scheme is a vof volume of fluid type method in the original thinc scheme one dimensional thinc scheme was straightforwardly used for multi dimensional cases in this paper we propose the wlic weighed line interface calculation method to extend the thinc scheme to multi dimension in the wlic method the interface is reconstructed by taking an average of line interfaces along x y and z coordinates with the weights calculated from surface normal the wlic method can extend the thinc scheme to multi dimension while maintaining simplicity of implementation and achieve a higher accuracy than the original thinc scheme the wlic method can readily extend the thinc scheme to three dimension

sharp interface immersed boundary level set method for wave body interactions a sharp interface cartesian grid method for the large eddy simulation of two phase turbulent flows interacting with moving bodies is presented the overall approach uses a sharp interface immersed boundary formulation and a level set ghost fluid method for solid fluid and fluid fluid interface treatments respectively a four step fractional step method is used for velocity pressure coupling and a lagrangian dynamic smagorinsky subgrid scale model is adopted for large eddy simulations a simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed a variety of test cases of different scales ranging from bubble dynamics water entry and exit landslide generated waves to ship hydrodynamics are performed for validation extensions for high reynolds number ship flows using wall layer models are also considered

a multi level adaptive mesh refinement for an integrated finite element level set formulation to simulate multiphase flows with surface tension abstract a multi level adaptive mesh refinement technique for an integrated finite element level set formulation was implemented to simulate the incompressible interfacial flows with surface tension by using unstructured p2p1 triangular and tetrahedral meshes linear quadratic elements near the interface were dynamically refined as an interface evolves in order to produce an accurate solution with a lower computational cost an adaptive mesh refinement algorithm for a linear element has been extended to a quadratic element by using a node reordering the proposed algorithm was successfully validated by solving several benchmark problems simulation of a static bubble problem was found to give an accurate solution with negligible spurious currents compared with existing results simulation results of rising bubble problems in 2d and 3d were also compared against existing numerical and experimental results in terms of terminal rising speed and terminal bubble shape we have found that the present algorithm provided stable and accurate solutions even for a high density ratio and that the solution accuracy strongly depended on the mesh resolution near the interface further the present algorithm was shown to be very efficient because the computational overhead by mesh refinement algorithm was very small compared to the elapsed times consumed for solving the incompressible navier stokes equations and the advection re initialization equations of level set method lastly the coalescence scenario of two oblique bubbles was well reproduced by the present 3d simulation

a monte carlo study of leading order scaling corrections of phi 4 theory on a three dimensional lattice we present a monte carlo study of the one component 4 model on a cubic lattice in three dimensions leading order scaling corrections are studied using the finite size scaling method we compute the corrections to scaling exponent with high precision we determine the value of the coupling at which leading order corrections to scaling vanish using this result we obtain estimates for critical exponents that are more precise than those obtained with field theoretic methods

a conservative phase field method for solving incompressible two phase flows in this paper a conservative phase field method based on the work of sun and beckermann y sun c beckermann sharp interface tracking using the phase field equation j comput phys 220 2007 626 653 for solving the two and three dimensional two phase incompressible navier stokes equations is proposed the present method can preserve the total mass as the cahn hilliard equation but the calculation and implementation are much simpler than that the dispersion relation preserving schemes are utilized for the advection terms while the helmholtz smoother is applied to compute the surface tension force term to verify the proposed method several benchmarks are examined and shown to have good agreements with previous results it also shows that the satisfactions of mass conservations are guaranteed

a high resolution mapped grid algorithm for compressible multiphase flow problems we describe a simple mapped grid approach for the efficient numerical simulation of compressible multiphase flow in general multi dimensional geometries the algorithm uses a curvilinear coordinate formulation of the equations that is derived for the euler equations with the stiffened gas equation of state to ensure the correct fluid mixing when approximating the equations numerically with material interfaces a c based and a a based model have been described that is an easy extension of the cartesian coordinates counterpart devised previously by the author 30 a standard high resolution mapped grid method in wave propagation form is employed to solve the proposed multiphase models giving the natural generalization of the previous one from single phase to multiphase flow problems we validate our algorithm by performing numerical tests in two and three dimensions that show second order accurate results for smooth flow problems and also free of spurious oscillations in the pressure for problems with interfaces this includes also some tests where our quadrilateral grid results in two dimensions are in direct comparisons with those obtained using a wave propagation based cartesian grid embedded boundary method

flip a method for adaptively zoned particle in cell calculations of fluid flows in two dimensions a method is presented for calculating fluid flow in two dimensions using a full particle in cell representation on an adaptively zoned grid the method has many interesting properties among them an almost total absence of numerical dissipation and the ability to represent large variations in the data the method is described using a standard formalism and its properties are illustrated by supersonic flow over a step and the interaction of a shock with a thin foil

a finite volume hllc based scheme for compressible interfacial flows with surface tension shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization similar behavior occurs inside of supersonic combustors scramjets under startup conditions but it is challenging to study these conditions experimentally in order to investigate this phenomenon further a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces the flow field is solved via the compressible multicomponent euler equations i e the five equation model discretized with the finite volume method on a uniform cartesian grid the solver utilizes a total variation diminishing tvd third order rungekutta method for time marching and second order tvd spatial reconstruction surface tension is incorporated using the continuum surface force csf model fluxes are upwinded with a modified hartenlaxvan leer contact hllc approximate riemann solver an interface compression scheme is employed to counter numerical diffusion of the interface the present work includes modifications to both the hllc solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gasliquid interface a simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non dimensionalization of the model the model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and mach 1 47 and 3 shock droplet interaction problems the general characteristics of secondary atomization at a range of weber numbers are also captured in a series of simulations

a sharp interface method for incompressible two phase flows we present a sharp interface method for computing incompressible immiscible two phase flows it couples the level set and volume of fluid techniques and retains their advantages while overcoming their weaknesses it is stable and robust even for large density and viscosity ratios on the order of 1000 to 1 the numerical method is an extension of the second order method presented by sussman m sussman a second order coupled levelset and volume of fluid method for computing growth and collapse of vapor bubbles journal of computational physics 187 2003 110 136 in which the previous method treated the gas pressure as spatially constant and the present method treats the gas as a second incompressible fluid the new method yields solutions in the zero gas density limit which are comparable in accuracy to the method in which the gas pressure was treated as spatially constant this improvement in accuracy allows one to compute accurate solutions on relatively coarse grids thereby providing a speed up over continuum or ghost fluid methods

error estimation and reduction with cross correlations besides the well known effect of autocorrelations in time series of monte carlo simulation data resulting from the underlying markov process using the same data pool for computing various estimates entails additional cross correlations this effect if not properly taken into account leads to systematically wrong error estimates for combined quantities using a straightforward recipe of data analysis employing the jackknife or similar resampling techniques such problems can be avoided in addition a covariance analysis allows for the formulation of optimal estimators with often significantly reduced variance as compared to more conventional averages

performance analysis on ldpc coded systems over quasi static mimo fading channels in this paper we derive closed form upper bounds on the error probability of low density parity check ldpc coded modulation schemes operating on quasi static fading channels the bounds are obtained from the so called fano gallager s tight bounding techniques and can be readily calculated when the distance spectrum of the code is available in deriving the bounds for multiple input multiple output mimo systems we assume the ldpc code is concatenated with the orthogonal space time block code as an inner code we obtain an equivalent single input single output siso channel model for this concatenated coded modulation system the upper bounds derived here indicate good matches with simulation results of a complete transceiver system over rayleigh and rician mimo fading channels in which the iterative detection and decoding algorithm is employed at the receiver

upper bounds to error probabilities of coded systems beyond the cutoff rate a family of upper bounds to error probabilities of coded systems was recently proposed by d divsalar see ieee communication theory workshop 1999 jpl tmo prog rep 42 139 1999 these bounds are valid for transmission over the additive white gaussian noise channel and require only the knowledge of the weight spectrum of the code words after illustrating these bounds we extend them to fading channels contrary to the union bound our bounds maintain their effectiveness below the signal to noise ratio snr at which the cutoff rate of the channel equals the rate of the code some applications are shown first we derive upper bounds to the minimum snr necessary to achieve zero error probability as the code block length increases to infinity next we use our bounds to predict the performance of turbo codes and low density parity check codes

robust second order accurate discretizations of the multi dimensional heaviside and dirac delta functions we present a robust second order accurate method for discretizing the multi dimensional heaviside and the dirac delta functions on irregular domains the method is robust in the following ways 1 integrations of source terms on a co dimension one surface are independent of the underlying grid and therefore stable under perturbations of the domain s boundary 2 the method depends only on the function value of a level function not on its derivatives we present the discretizations in tabulated form to make their implementations straightforward we present numerical results in two and three spatial dimensions to demonstrate the second order accuracy in the l 1 norm in the case of the solution of pdes with singular source terms in the case of evaluating the contribution of singular source terms on interfaces the method is also second order accurate in the l norm

a contoured continuum surface force model for particle methods a surface tension model is essential to simulate multiphase flows with deformed interfaces this study develops a contoured continuum surface force ccsf model for particle methods a color function that varies sharply across the interface to mark different fluid phases is smoothed in the transition region where the local contour curvature can be regarded as the interface curvature the local contour passing through each reference particle in the transition region is extracted from the local profile of the smoothed color function the local contour curvature is calculated based on the taylor series expansion of the smoothed color function whose derivatives are calculated accurately according to the definition of the smoothed color function two schemes are proposed to specify the smooth radius fixed scheme where 2 r e r e particle interaction radius is assigned to all particles in the transition region and varied scheme where r e and 2 r e are assigned to the central and edged particles in the transition region respectively numerical examples including curvature calculation for static circle and ellipse interfaces deformation of square droplet to a circle 2d and 3d droplet deformation in shear flow and droplet coalescence are simulated to verify the ccsf model and compare its performance with those of other methods the ccsf model with the fixed scheme is proven to produce the most accurate curvature and lowest parasitic currents among the tested methods

a conservative level set method for contact line dynamics a new model for simulating contact line dynamics is proposed we apply the idea of driving contact line movement by enforcing the equilibrium contact angle at the boundary to the conservative level set method for incompressible two phase flow e olsson g kreiss a conservative level set method for two phase flow j comput phys 210 2005 225 246 a modified reinitialization procedure provides a diffusive mechanism for contact line movement and results in a smooth transition of the interface near the contact line without explicit reconstruction of the interface we are able to capture contact line movement without loosing the conservation numerical simulations of capillary dominated flows in two space dimensions demonstrate that the model is able to capture contact line dynamics qualitatively correct

a higher order accurate surface tension modelling volume of fluid scheme for 2d curvilinear meshes abstract this paper proposes a higher order accurate curvature calculation method for volume of fluid vof based surface tension modelling on 2d curvilinear meshes the scheme extends the interface reconstruction component of the height function hf method to curvilinear meshes in 2d linear reconstructions are computed in each column overlapping the interface which results in a piecewise linear plic representation of the free surface this is done in a volume conservative manner by employing a novel sweep line algorithm the interface curvature is then computed analytically by fitting either second or fourth order polynomials to local stencils of plic facets formal second and fourth order accuracy of interface curvature is demonstrated by comparing numerical results with a variety of analytical interface definitions the curvature algorithm is implemented into a balanced force continuum surface force surface tension scheme for variable density flows second and fourth order accuracy are again demonstrated for the laplace pressure jump in the simulation of a stationary bubble with a high liquid gas density ratio lastly second order accuracy is demonstrated in computing the frequency of an inviscid oscillating droplet in zero gravity

a lattice boltzmann method for axisymmetric multicomponent flows with high viscosity ratio a color gradient lattice boltzmann method lbm is proposed to simulate axisymmetric multicomponent flows this method uses a collision operator that is a combination of three separate parts namely single component collision operator perturbation operator and recoloring operator a source term is added into the single component collision operator such that in each single component region the axisymmetric continuity and momentum equations can be exactly recovered the interfacial tension effect is realized by the perturbation operator in which an interfacial force of axisymmetric form is derived using the concept of continuum surface force a recoloring operator proposed by latva kokko and rothman is extended to the axisymmetric case for phase segregation and maintenance of the interface to enhance the method s numerical stability for handling binary fluids with high viscosity ratio a multiple relaxation time model is used for the collision operator several numerical examples including static droplet test oscillation of a viscous droplet and breakup of a liquid thread are presented to test the capability and accuracy of the proposed color gradient lbm it is found that the present method is able to accurately capture the phase interface and produce low spurious velocities also the lbm results are all in good agreement with the analytical solutions and or available experimental data for a very broad range of viscosity ratios a color gradient lbm is developed for immiscible axisymmetric multiphase flows the method consists of three separate operators in which axisymmetric effects are considered the method is demonstrated to be accurate for a very wide range of viscosity ratios viscosity ratio is found to affect significantly growth of rayleigh instability but have negligible effect on droplet size

direct numerical simulation of evaporating droplets a model for the three dimensional direct numerical simulation of evaporating deforming droplets in incompressible flow is presented it is based on the volume of fluid method and is therefore capable of capturing very strong deformations the evaporation rate is computed based on the vapour mass fraction and the plic reconstruction of the surface emphasis is put on the correct calculation of the velocities of the gaseous and liquid phase at the interface which is very important for cases with high mass transfer rates and thus high stefan flow it is accomplished by the use of an iterative algorithm that enforces a divergence constraint in cells containing the interface validation comprises a 1d test case for interfacial mass transfer droplet collisions and oscillations as well as calculation of sherwood numbers for two different cases of evaporating droplets where low and high mass transfer rates occur comparison with data from the literature shows good agreement of the obtained results the simulation of a strongly deformed water droplet in a flow at a high reynolds and weber number is used to demonstrate the capabilities of the presented method the emerging flow field in the wake of the droplet is very complex and three dimensional

two phase electrohydrodynamic simulations using a volume of fluid approach a numerical methodology to simulate two phase electrohydrodynamic flows under the volume of fluid paradigm is proposed the electric force in such systems acts only at the interface and is zero elsewhere in the two fluids continuum surface force representations are derived for the electric field force in a system of dielectric dielectric and conducting conducting fluids on the basis of analytical calculations for simple flow problems we propose a weighted harmonic mean interpolation scheme to smoothen the electric properties in the diffused transition region interface it is shown that a wrong choice of interpolation scheme weighted arithmetic mean may lead to a transition region thickness dependent electric field in the bulk we simulate a set of problems with exact or approximate analytical solutions to validate the numerical model proposed a coupled level set and volume of fluid clsvof algorithm has been used for simulations presented here

level set reinitialization at a contact line when a level set signed distance function is reinitialized in the vicinity of a contact line there is a blind spot that prevents an accurate reconstruction of a signed distance function the numerical method can create parasitic velocity currents near this region if additional contact line physics are included the parasitic velocity currents would pollute the solution and alter the physical behavior in this study a modified reinitialization routine is proposed that combines the standard hamilton jacobi equation with a relaxation equation for those grid cells along a wall in the blind spot two test cases an angled fluid wedge zero curvature and a circular fluid arc constant curvature are used to evaluate the numerical error induced by different methods the proposed method has less numerically induced interface distortion than other techniques examined furthermore this routine can be easily extended to three dimensions drops sliding on a wall are simulated in both two and three dimensions to demonstrate the advantages of this method a spreading fluid interface further shows that this method allows contact lines to merge naturally

gradient augmented level set method for phase change simulations abstract a numerical method for the simulation of two phase flow with phase change based on the gradient augmented level set gals strategy is presented sharp capturing of the vaporization process is enabled by i identification of the vapor liquid interface t at the subgrid level ii discontinuous treatment of thermal physical properties except for and iii enforcement of mass momentum and energy jump conditions where the gradients of the dependent variables are obtained at t and are consistent with their analytical expression i e no local averaging is applied treatment of the jump in velocity and pressure at t is achieved using the ghost fluid method the solution of the energy equation employs the sub grid knowledge of t to discretize the temperature laplacian using second order one sided differences i e the numerical stencil completely resides within each respective phase to carefully evaluate the benefits or disadvantages of the gals approach the standard level set method is implemented and compared against the gals predictions the results show the expected trend that interface identification and transport are predicted noticeably better with gals over the standard level set this benefit carries over to the prediction of the laplacian and temperature gradients in the neighborhood of the interface which are directly linked to the calculation of the vaporization rate however when combining the calculation of interface transport and reinitialization with two phase momentum and energy the benefits of gals are to some extent neutralized and the causes for this behavior are identified and analyzed overall the additional computational costs associated with gals are almost the same as those using the standard level set technique

a monotonicity preserving conservative sharp interface flow solver for high density ratio two phase flows this paper presents a novel approach for solving the conservative form of the incompressible two phase navier stokes equations in order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface the proposed method includes a volume of fluid type integration of the convective momentum transport a monotonicity preserving momentum rescaling and a consistent and conservative ghost fluid projection that includes surface tension effects the numerical dissipation inherent in the volume of fluid treatment of the convective transport is localized in the interface vicinity enabling the use of a kinetic energy conserving discretization away from the singularity two and three dimensional tests are presented and the solutions shown to remain accurate at arbitrary density ratios the proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization

a hybrid level set front tracking approach for finite element simulations of two phase flows abstract in this paper we give details on the numerical realization of a new finite element method for the simulation of two phase flows which was recently introduced in basting and weismann 2013 the main ingredient is a hybrid representation of the interface between the fluid phases an implicit description of the interface is given by a level set function and an explicit representation is obtained from aligning edges of the computational mesh to the implicitly described interface this step is done by a black box optimization based mesh smoothing approach which does not change the topology of the mesh while guaranteeing optimal mesh quality furthermore we make use of quadratic isoparametric elements to increase the approximation quality of the discrete interface due to the alignment discontinuities of the solution variables pressure can be captured accurately while a variational treatment of the curvature allows for a precise approximation of surface tension we present our time discretization scheme for the coupled navier stokes level set equations and discuss our space discretization based on the so called subspace projection method spm to account for discontinuities across the interface we present two numerical examples for which reference solutions exist we consider the oscillation of a single droplet and provide our results for an established two phase flow benchmark problem

phase field computations for ternary fluid flows we present a new phase field model for three component immiscible liquid flows with surface tension in the phase field approach the classical sharp interface between the two immiscible fluids is replaced by a transition region across which the properties of fluids change continuously the proposed method incorporates a chemical potential which can eliminate the unphysical phase field profile and a continuous surface tension force formulation from which we can calculate the pressure field directly from the governing equations the capabilities of the method are demonstrated with several examples we compute the ternary phase separation via spinodal decomposition equilibrium phase field profiles pressure field distribution and a three interface contact angle resulting from a spreading liquid lens on an interface the numerical results show excellent agreement with analytical solutions

variations on the gallager bounds connections and applications there has been renewed interest in deriving tight bounds on the error performance of specific codes and ensembles based on their distance spectrum we discuss many reported upper bounds on the maximum likelihood ml decoding error probability and demonstrate the underlying connections that exist between them in addressing the gallager bounds and their variations we focus on the duman and salehi see ieee trans commun vol 46 p 717 723 1998 variation which originates from the standard gallager bound a large class of efficient bounds or their chernoff versions is demonstrated to be a special case of the generalized second version of the duman and salehi bounds implications and applications of these observations are pointed out including the fully interleaved fading channel resorting to either matched or mismatched decoding the proposed approach can be generalized to geometrically uniform nonbinary codes finite state channels bit interleaved coded modulation systems and it can be also used for the derivation of upper bounds on the conditional decoding error probability

anisotropic mesh adaptation with optimal convergence for finite elements using embedded geometries this paper presents a numerical study of a recent technique that consists in modeling embedded geometries by a level set representation in combination with local anisotropic mesh refinement the local anisotropic mesh procedure is suitable for various orders p of finite element approximations this method proves beneficial in simulations involving complex geometries as it suppresses the need for the tedious process of body fitted mesh generation without altering the finite element formulation nor the prescription of boundary conditions the first part of the study deals with a simple laplace problem featuring a planar interface on which a dirichlet boundary condition is imposed it is shown that the appropriate amount of local isotropic refinement yields the optimal convergence rate for various finite element orders p unlike uniform refinement anisotropic refinement further ensures geometric convergence and limits the growth of the number of unknowns then we explain how to use metric based anisotropic adaptation to obtain nearly body fitted meshes with arbitrary geometries the optimal rate of convergence both for the solution and the geometry is demonstrated on 2d and 3d academic laplace problems involving curved boundaries finally applications in the field of fluid dynamics and material science are presented the results for these simulations successfully converge towards data from the literature analytical solutions or values obtained with body fitted meshes

a direct comparison between volume and surface tracking methods with a boundary fitted coordinate transformation and third order upwinding a volume tracking vt and a front tracking ft algorithm are implemented and compared for locating the interface between two immiscible incompressible newtonian fluids in a tube with a periodically varying circular cross section initially the fluids are stationary and stratified in an axisymmetric arrangement so that one is around the axis of the tube core fluid and the other one surrounds it annular fluid a constant pressure gradient sets them in motion with both vt and ft a boundary fitted coordinate transformation is applied and appropriate modifications are made to adopt either method in this geometry the surface tension force is approximated using the continuous surface force method all terms appearing in the continuity and momentum equations are approximated using centered finite differences in space and one sided forward finite differences in time in each time step the incompressibility condition is enforced by a transformed poisson equation which is linear in pressure this equation is solved by either direct lu decomposition or a multigrid iterative solver when the two fluids have the same density the former method is about 3 5 times faster but when they do not the multigrid solver is as much as 10 times faster than the lu decomposition when the interface does not break and the reynolds number remains small the accuracy and rates of convergence of vt and ft are comparable the well known failure of centered finite differences arises as the reynolds number increases and leads to non physical oscillations in the interface and failure of both methods to converge with mesh refinement these problems are resolved and computations with reynolds as large as 500 converged by approximating the convective terms in the momentum equations by third order upwind differences using lagrangian polynomials when the volume of the core fluid or the weber number decrease increasing the importance of interfacial tension and leading to breakup of the interface forming a drop of core fluid the ft method converges faster with mesh refinement than the vt method and upwinding may be required finally examining the generation of spurious currents around a stationary bubble in the tube for ohnesorge numbers between 0 1 and 10 it is found that the maximum velocity remains approximately the same in spite mesh refinements when vt is applied whereas it is of the same order of magnitude for the coarsest mesh and monotonically decreases with mesh refinement when ft is applied

a fast pressure correction method for incompressible two fluid flows we have developed a new pressure correction method for simulating incompressible two fluid flows with large density and viscosity ratios the method s main advantage is that the variable coefficient poisson equation that arises in solving the incompressible navier stokes equations for two fluid flows is reduced to a constant coefficient equation which can be solved with an fft based fast poisson solver this reduction is achieved by splitting the variable density pressure gradient term in the governing equations the validity of this splitting is demonstrated from our numerical tests and it is explained from a physical viewpoint in this paper the new pressure correction method is coupled with a mass conserving volume of fluid method to capture the motion of the interface between the two fluids but in general it could be coupled with other interface advection methods such as level set phase field or front tracking first we verified the new pressure correction method using the capillary wave test case up to density and viscosity ratios of 10 000 then we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value next the method is shown to be second order accurate in space and time independent of the vof method and it conserves mass momentum and kinetic energy in the inviscid limit also we show that for solving the two fluid navier stokes equations the method is 10 40 times faster than the standard pressure correction method which uses multigrid to solve the variable coefficient poisson equation finally we show that the method is capable of performing fully resolved direct numerical simulation dns of droplet laden isotropic turbulence with thousands of droplets using a computational mesh of 1024 3 points

improvement of monte carlo estimates with covariance optimized finite size scaling at fixed phenomenological coupling in the finite size scaling analysis of monte carlo data instead of computing the observables at fixed hamiltonian parameters one may choose to keep a renormalization group invariant quantity also called phenomenological coupling fixed at a given value within this scheme of finite size scaling we exploit the statistical covariance between the observables in a monte carlo simulation in order to reduce the statistical errors of the quantities involved in the computation of the critical exponents this method is general and does not require additional computational time this approach is demonstrated in the ising model in two and three dimensions where large gain factors in cpu time are obtained

a sharp interface method for sph a sharp interface method sim for smoothed particle hydrodynamics sph has been developed to simulate two phase flows with clear interfaces the level set function is introduced to capture the interface implicitly the interface velocity is used to evolve the level set function the smoothness of the level set function helps to improve the accuracy of the interface curvature material discontinuity across the interface is dealt with by the ghost fluid method the interface states are calculated by applying the jump conditions and are extended to the corresponding ghost fluid particles the ghost fluid method helps to get smooth and stable calculation near the interface the performance of the developed method is validated by benchmark tests the developed sim for sph can be applied to simulate low speed two phase flows of high density ratios with clear interface accurately and stably

time integration for diffuse interface models for two phase flow we propose a variant of the q scheme for diffuse interface models for two phase flow together with three new linearization techniques for the surface tension these involve either additional stabilizing force terms or a fully implicit coupling of the navier stokes and cahn hilliard equation in the common case that the equations for interface and flow are coupled explicitly we find a time step restriction which is very different to other two phase flow models and in particular is independent of the grid size we also show that the proposed stabilization techniques can lift this time step restriction even more pronounced is the performance of the proposed fully implicit scheme which is stable for arbitrarily large time steps we demonstrate in a taylor flow application that this superior coupling between flow and interface equation can decrease the computation time by several orders of magnitude

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

analysis of a stokes interface problem we consider a stationary stokes problem with a piecewise constant viscosity coefficient for the variational formulation of this problem we prove a well posedness result in which the constants are uniform with respect to the jump in the viscosity coefficient we apply a standard discretization with a pair of lbb stable finite element spaces the main result of the paper is an infsup result for the discrete problem that is uniform with respect to the jump in the viscosity coefficient from this we derive a robust estimate for the discretization error we prove that the mass matrix with respect to some suitable scalar product yields a robust preconditioner for the schur complement results of numerical experiments are presented that illustrate this robustness property

an extended finite element method applied to levitated droplet problems we consider a standard model for incompressible two phase flows in which a localized force at the interface describes the effect of surface tension if a level set method is applied then the approximation of the interface is in general not aligned with the triangulation this causes severe difficulties w r t the discretization and often results in large spurious velocities in this paper we reconsider a modified extended finite element method xfem which in previous papers has been investigated for relatively simple two phase flow model problems and apply it to a physically realistic levitated droplet problem the results show that due to the extension of the standard fe space one obtains much better results in particular for large interface tension coefficients furthermore a certain cut off technique results in better efficiency without sacrificing accuracy copyright 2010 john wiley sons ltd

analysis of the incompressibility constraint in the smoothed particle hydrodynamics method summary smoothed particle hydrodynamics sph is a particle based fully lagrangian method for fluid flow simulations in this work fundamental concepts of the method are first briefly recalled then we present a thorough comparison of two different incompressibility treatments in sph the weakly compressible approach where a suitably chosen equation of state is used and the truly incompressible method in two basic variants where the velocity field projection onto a divergence free space is performed a noteworthy aspect of the study is that in each incompressibility treatment the same boundary conditions are used and further developed that allows a direct comparison to be made two dimensional and three dimensional validation cases are studied problems associated with the numerical setup are discussed and an optimal choice of the computational parameters is proposed and verified the efficiency issues of the incompressibility treatments are considered and the speed up features are highlighted the results show that the present state of the art truly incompressible methods based on a velocity correction suffer from density accumulation errors to address this issue an algorithm based on a correction for both particle velocities and positions is presented the usefulness of this density correction is examined and demonstrated copyright 2012 john wiley sons ltd

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

performance bounds for turbo coded modulation systems we apply the standard union bound to turbo coded modulation systems with maximum likelihood decoding to illustrate the methodology we explicitly derive the bounds for the 2 bits s hz 16 qam system generalization of this bound to other turbo coded modulation systems is straightforward as in the case of the standard union bound for turbo codes we expect these bounds to be useful for rather large values of signal to noise ratios i e signal to noise ratios for which the code rate is smaller than the corresponding cutoff rate the bound is based on uniform interleaving just as its counterpart for standard turbo coding the derived bound provides a tool for comparing coded modulation schemes having different component codes interleaver lengths mappings etc using maximum likelihood decoding it is also useful in studying the effectiveness of various suboptimal decoding algorithms the bounding technique is also applicable to other coded modulation schemes such as serially concatenated coded modulation

modeling surface tension in compressible flow on an adaptively refined mesh abstract we present a numerical approach to model surface tension between immiscible materials within an inviscid compressible flow solver the material interface is represented using the volume of fluid technique with piecewise linear interface reconstructions we employ the continuum surface force to model surface tension and have implemented it in the context of the muscl hancock finite volume method for the euler equations on an adaptively refined eulerian mesh we show results from droplet verification tests the rayleigh taylor instability linear regime and simulate a 2d shock droplet interaction

a semi implicit level set method for multiphase flows and fluid structure interaction problems in this paper we present a novel semi implicit time discretization of the level set method introduced in 8 for fluid structure interaction problems the idea stems from a linear stability analysis derived on a simplified one dimensional problem the semi implicit scheme relies on a simple filter operating as a pre processing on the level set function it applies to multiphase flows driven by surface tension as well as to fluid structure interaction problems the semi implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost it is validated through comparisons with the original explicit scheme and refinement studies on two dimensional benchmarks

an adaptive variational procedure for the conservative and positivity preserving allen cahn phase field model abstract in this paper we present an adaptive variational procedure for unstructured meshes to capture fluid fluid interfaces in two phase flows the two phases are modeled by the phase field finite element formulation which involves the conservative allen cahn equation coupled with the incompressible navier stokes equations the positivity preserving variational formulation is designed to maintain the bounded and stable solution of the allen cahn equation for the adaptivity procedure we consider the residual based error estimates for the underlying differential equations of the two phase system in particular the adaptive refinement coarsening is carried out by the newest vertex bisection algorithm by evaluating the residual error indicators based on the error estimates of the allen cahn equation the coarsening algorithm avoids the storage of the tree data structures for the hierarchical mesh thus providing the ease of numerical implementation furthermore the proposed nonlinear adaptive partitioned procedure aims at reducing the amount of coarsening while maintaining the convergence properties of the underlying nonlinear coupled differential equations we investigate the adaptive phase field finite element scheme through the spinodal decomposition in a complex curved geometry and the volume conserved interface motion driven by the mean curvature flow for two circles in a square domain we then assess the accuracy and efficiency of the proposed procedure by modeling the free surface motion in a sloshing tank in contrast to the non adaptive eulerian grid counterpart we demonstrate that the mesh adaptivity remarkably reduces the degrees of freedom and the computational cost by nearly half for similar accuracy the mass loss in the allen cahn equation via adaptivity process is also reduced by nearly three times compared to the non adaptive mesh finally we apply the adaptive numerical framework to solve the application of a dam breaking problem with topological changes

regular article calculation of two phase navier stokes flows using phase field modeling phase field models provide a way to model fluid interfaces as having finite thickness this can allow the computation of interface movement and deformation on fixed grids this paper applies phase field modeling to the computation of two phase incompressible navier stokes flows the navier stokes equations are modified by the addition of the continuum forcing email protected f where c is the composition variable and f is c s chemical potential the equation for interface advection is replaced by a continuum advective diffusion equation with diffusion driven by c s chemical potential gradients the paper discusses how solutions to these equations approach those of the original sharp interface navier stokes equations as the interface thickness e and the diffusivity both go to zero the basic flow physics of phase field interfaces is discussed straining flows can thin or thicken an interface and this must be resisted by a high enough diffusion on the other hand too large a diffusion will overly damp the flow these two constraints result in an upper bound for the diffusivity of o e and a lower bound of o e 2 within these two bounds the phase field navier stokes equations appear to generate an o e error relative to the exact sharp interface equations an o h 2 e 2 numerical method is introduced that is energy conserving in the sense that creation of interface energy by convection is always balanced by an equal decrease in kinetic energy caused by surface tension forcing an o h 4 e 4 compact scheme is introduced that takes advantage of the asymptotic comparatively smooth behavior of the chemical potential for o e accurate phase field models the optimum path to convergence for this scheme appears to be email protected 4 5 the asymptotic rate of convergence corresponding to this is o h 4 5 but results at practical resolutions show that the practical convergence of the method is generally considerably faster than linear extensive analysis and computations show that this scheme is very effective and accurate it allows the accurate calculation of two phase flows with interfaces only two cells wide computational results are given for linear capillary waves and for rayleigh taylor instabilities the first set of computations is compared to exact solutions of the diffuse interface equations and of the original sharp interface equations the rayleigh taylor computations test the ability of the method to compute highly deforming flows these flows include near singular phenomena such as interface coalescences and breakups contact line movement and the formation and breakup of thin wall films grid refinement studies are made and rapid convergence is found for macroscopic flow features such as instability growth rate and propagation speed wavelength and the general physical characteristics of the instability and mass transfer rates

an all speed relaxation scheme for interface flows with surface tension we consider interface flows where compressibility and capillary forces surface tension are significant these flows are described by a non conservative unconditionally hyperbolic multiphase model the numerical approximation is based on finite volume method for unstructured grids at the discrete level the surface tension is approximated by a volume force csf formulation the interface physical properties are recovered by designing an appropriate linearized riemann solver relaxation scheme that prevents spurious oscillations near material interfaces for low speed flows a preconditioning linearization is proposed and the low mach asymptotic is formally recovered numerical computations for a bubble equilibrium converge to the required laplace law and the dynamic of a drop falling under gravity is in agreement with experimental observations

a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

random coding techniques for nonrandom codes this work provides techniques to apply the channel coding theorem and the resulting error exponent which was originally derived for totally random block code ensembles to ensembles of codes with less restrictive randomness demands as an example the random coding technique can even be applied for an ensemble that contains a single code for a specific linear code we get an upper bound for the error probability which equals gallager s 1968 random coding bound up to a factor determined by the maximum ratio between the weight distribution of the code and the expected random weight distribution

tight exponential upper bounds on the ml decoding error probability of block codes over fully interleaved fading channels we derive tight exponential upper bounds on the decoding error probability of block codes which are operating over fully interleaved rician fading channels coherently detected and maximum likelihood decoded it is assumed that the fading samples are statistically independent and that perfect estimates of these samples are provided to the decoder these upper bounds on the bit and block error probabilities are based on certain variations of the gallager bounds these bounds do not require integration in their final version and they are reasonably tight in a certain portion of the rate region exceeding the cutoff rate of the channel by inserting interconnections between these bounds we show that they are generalized versions of some reported bounds for the binary input additive white gaussian noise channel

a fixed grid sharp interface method for bubble dynamics and phase change abstract a numerical method has been developed for direct simulation of bubble dynamics with large liquid to vapor density ratio and phase change the numerical techniques are based on a fixed grid finite volume method capable of treating the interface as a sharp discontinuity the unsteady axisymmetric navier stokes equations and energy equation in both liquid and vapor phases are computed the mass momentum and energy conditions are explicitly matched at the phase boundary to determine the interface shape and movement the cubic b spline is used in conjunction with a fairing algorithm to yield smooth and accurate information of curvatures nondimensional parameters including reynolds weber and jakob numbers are varied to offer insight into the physical and numerical characteristics of the bubble dynamics based on the present sharp interface approach bubble dynamics for density ratio of 1600 or higher with and without phase change can be successfully computed

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes

a high resolution characteristics based implicit dual time stepping vof method for free surface flow simulation on unstructured grids in this paper a new unstructured grid finite volume incompressible navier stokes solver based on a high order characteristics based method the artificial compressibility method and a matrix free implicit dual time stepping scheme has been developed to study unsteady free surface flows the free surface effects are calculated using the volume of fluid vof method and continuum surface force the transport equation for the vof is numerically solved using exactly the same method for the flow solver a number of test cases have been studied to validate the proposed method and demonstrate its capability by comparison with other schemes and published results