extension of finite volume compressible flow solvers to multi dimensional variable density zero mach number flows when attempting to compute unsteady variable density flows at very small or zero mach number using a standard finite volume compressible flow solver one faces at least the following difficulties i spatial pressure variations vanish as the mach numberm

coupling an eulerian fluid calculation to a lagrangian solid calculation with the ghost fluid method we propose a numerical method for modeling multimaterial flows where the domain is decomposed into separate eulerian and lagrangian subdomains that is the equations are written in eulerian form in one subdomain and in lagrangian form in the other subdomain this is of interest for example when considering the effect of underwater explosions on the hull of a ship or the impact of a low speed projectile on a soft explosive target on the one hand high speed fluid flows are traditionally modeled by applying shock capturing schemes to the compressible euler equations to avoid problems associated with tangling of a lagrangian mesh on the other hand solid dynamics calculations are traditionally carried out using lagrangian numerical methods to avoid problems associated with numerical smearing in eulerian calculations we use the ghost fluid method to create accurate discretizations across the eulerian lagrangian interface the numerical method is presented in both one and two spatial dimensions three dimensional extensions to the interface coupling method are straightforward

duality for modules over finite rings and applications to coding theory this paper sets a foundation for the study of linear codes over finite rings the finite frobenius rings are singled out as the most appropriate for coding theoretic purposes because two classical theorems of mac williams the extension theorem and the mac williams identities generalize from finite fields to finite frobenius rings it is over frobenius rings that certain key identifications can be made between the ring and its complex characters

three dimensional front tracking we describe a three dimensional front tracking algorithm discuss its numerical implementation and present studies to validate the correctness of this approach based on the results of the two dimensional computations we expect three dimensional front tracking to significantly improve computational efficiencies for problems dominated by discontinuities in some cases for which the interface computations display considerable numerical sensitivity we expect a greatly enhanced capability

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

crystal growth and dendritic solidification we present a numerical method which computes the motion of complex solid liquid boundaries in crystal growth the model we solve includes physical effects such as crystalline anisotropy surface tension molecular kinetics and undercooling the method is based on two ideas first the equations of motion are recast as a single history dependent boundary integral equation on the solid liquid boundary a fast algorithm is used to solve the integral equation efficiently second the boundary is moved by solving a hamiltonjacobi type equation on a fixed domain formulated by osher and sethian for a function in which the boundary is a particular level set this equation is solved by finite difference schemes borrowed from the technology of hyperbolic conservation laws the two ideas are combined by constructing a smooth extension of the normal velocity off the moving boundary in a way suggested by the physics of the problem our numerical experiments show the evolution of complex crystalline shapes development of large spikes and corners dendrite formation and side branching and pieces of solid merging and breaking off freely

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

computing interface motion in compressible gas dynamics a hamilton jacobi level set formulation of the equations of motion for propagating interfaces has been introduced recently by osher and sethian this formulation allows fronts to self intersect develop singularities and change topology the numerical algorithms based on this approach handle topological merging and breaking naturally work in any number of space dimensions and do not require that the moving front be written as a function instead the moving front is embedded as a particular level set in a fixed domain partial differential equation numerical techniques borrowed from hyperbolic conservation laws are then used to accurately capture the complicated surface motion that satisfies the global entropy condition for propagating fronts given by sethian in this paper we analyze the coupling of this level set formulation to a system of conservation laws for compressible gas dynamics we study both conservative and non conservative differencing of the level set function and compare the two approaches to illustrate the capability of the method we study the compressible rayleigh taylor and kelvin helmholtz instabilities for air air and air helium boundaries we perform numerical convergence studies of the method over a range of parameters and analyze the accuracy of this approach applied to these problems

decoding of linear codes over galois rings we present a method for decoding an arbitrary linear code over a galois ring spl rscr by a process of lifting decoding algorithms for a family of linear codes over a finite field spl kscr forming an spl alpha element chain where spl kscr is the quotient field of spl rscr and spl rscr has characteristic p sup spl alpha as a new result this method also works for linear codes over spl rscr which are nonfree spl rscr modules

a numerical method for three dimensional gas liquid flow computations a numerical method for multiphase flow computations based on a finite difference formulation with a fixed grid is described the method combines ideas from front tracking and the ghost fluid method with a numerical technique for velocity extrapolation near the interface it is shown that the method is able to solve three dimensional free surface flow problems with an incompressible liquid and a compressible gas maintaining the interface sharp numerical results are compared with numerical solutions of the rayleigh plesset equation for the free oscillation of a gas bubble and independent front tracking results for buoyant bubbles finally the effects of an imposed sinusoidal liquid flow on a gas bubble are investigated

a discontinuous galerkin method for the simulation of compressible gas gas and gas water two medium flows abstract in this paper we develop a new discontinuous galerkin method for the simulation of shocks and interfaces in compressible gas gas and gas water two medium flows by solving the based model the spatial discretization is carefully designed to possess the following features discrete conservation in terms of the total mass total momentum and total energy high order accuracy and consistency for smooth flows free of oscillations at an isolated material interface in order to handle potential discontinuities arising in the simulation a nonlinear limiter based on the weighted essentially non oscillatory weno strategy is employed to suppress numerical oscillations and to preserve high order of accuracy in regions of smooth flows the weno reconstruction is imposed on suitably selected quantities rather than the conserved ones in case for discontinuities with large pressure ratio low density and dramatic change of material property where unphysical variables may be encountered a posteriori solution correction on the subcell level is locally adopted to enhance the robustness a series of typical test cases for both one and two dimensional problems are provided to demonstrate the performance of the proposed method

semi implicit extension of a godunov type scheme based on low mach number asymptotics i one dimensional flow a single scale multiple space scale asymptotic analysis provides detailed insight into the low mach number limit behavior of solutions of the compressible euler equations we use the asymptotics as a guideline for developing a low mach number extension of an explicit higher order shock capturing scheme this semi implicit scheme involves multiple pressure variables large scale differencing and averaging procedures that are discretized versions of standard operations in multiple scales asymptotic analysis advection and acoustic wave propagation are discretized explicitly and upwind and only one scalar elliptic equation is to be solved implicitly at each time step this equation is a pressure correction equation for incompressible flows when the mach number is zero in the low mach number limit the time step is restricted by a courant number based essentially on the maximum flow velocity for moderate and large mach numbers the scheme reduces to the underlying explicit higher order shock capturing algorithm

linear diophantine equations over polynomials and soft decoding of reed solomon codes this paper generalizes the classical knuth schoumlnhage algorithm computing the greatest common divisor gcd of two polynomials for solving arbitrary linear diophantine systems over polynomials in time quasi linear in the maximal degree as an application the following weighted curve fitting problem is considered given a set of points in the plane find an algebraic curve satisfying certain degree conditions that goes through each point the prescribed number of times the main motivation for this problem comes from coding theory namely it is ultimately related to the list decoding of reed solomon codes this paper presents a new fast algorithm for the weighted curve fitting problem based on the explicit construction of a groebner basis this gives another fast algorithm for the soft decoding of reed solomon codes different from the procedure proposed by feng which works in time w r o 1 nlog2n where r is the rate of the code and w is the maximal weight assigned to a vertical line

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

multicomponent flow calculations by a consistent primitive algorithm the dynamics of inviscid multicomponent fluids may be modelled by the euler equations augmented by one or more additional species equation s attempts to compute solutions for extended euler models in conservation form show strong oscillations and other computational inaccuracies near material interfaces these are due to erroneous pressure fluctuations generated by the conservative wave model this problem does not occur in single component computations and arises only in the presence of several species a nonconservative primitive euler formulation is proposed which results in complete elimination of the oscillations the numerical algorithm uses small viscous perturbations to remove leading order conservation errors and is conservative to the order of numerical approximation numerical experiments show clean monotonic solution profiles with acceptably small conservation error for shocks of weak to moderate strengths

numerical simulation of liquid gas phase flow during mold filling abstract a numerical model for simulation of liquid gas phase flow during mold filling is presented the incompressible navier stokes equations are discretized on a fixed cartesian mesh with finite difference method the fractional step scheme is employed for enforcing incompressibility constraint the free surface effects are calculated using the volume of fluid method based on the piecewise linear interface reconstruction and split lagrangian advection of volume fraction field adding limited compressibility to the gas phase led to improvement in convergence rate of poisson equation solver about 2 fold this new concept permits simulation of two phase incompressible free surface flow during mold filling without using outflow boundary condition numerical results are presented for several test cases which demonstrate validity capability and performance of the proposed method in contrast with the traditional fully incompressible approach

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

a new method for finite element transitional mesh generation in the preparation of finite element meshes inclusion of transitional blocks is important in order to construct optimal meshes in this paper a new method is proposed which is capable of generating quaddominated arbitrary transitional meshes these meshes are well graded and do not require any mesh smoothening algorithm the inverse isoparametric mapping combined with an elimination procedure is used to construct transition zones this new algorithm is described in detail and its efficiency is illustrated with appropriate examples different methods available for inverse isoparametric mapping are discussed with their merits and limitations many of the existing techniques for inverse isoparametric mapping require the calculation of some special coefficients which may vary with the element type these techniques lose their clarity and efficiency in the case of three dimensional and higher order two dimensional elements in this paper a generalized iterative procedure is proposed to carry out the inverse isoparametric mapping the computations in this approach are already part of every finite element program based on the isoparametric formulation hence implementation of the new algorithm is very simple and straightforward

improved decoding of reed solomon and algebraic geometry codes given an error correcting code over strings of length n and an arbitrary input string also of length n the list decoding problem is that of finding all codewords within a specified hamming distance from the input string we present an improved list decoding algorithm for decoding reed solomon codes the list decoding problem for reed solomon codes reduces to the following curve fitting problem over a field f given n points x sub i spl middot y sub i sub i 1 sup n x sub i y sub i spl isin f and a degree parameter k and error parameter e find all univariate polynomials p of degree at most k such that y sub i p x sub i for all but at most e values of i spl isin 1 n we give an algorithm that solves this problem for e 1 3 where the result yields the first asymptotic improvement in four decades the algorithm generalizes to solve the list decoding problem for other algebraic codes specifically alternant codes a class of codes including bch codes and algebraic geometry codes in both cases we obtain a list decoding algorithm that corrects up to n spl radic n n d errors where n is the block length and d is the designed distance of the code the improvement for the case of algebraic geometry codes extends the methods of shokrollahi and wasserman see in proc 29th annu acm symp theory of computing p 241 48 1998 and improves upon their bound for every choice of n and d we also present some other consequences of our algorithm including a solution to a weighted curve fitting problem which may be of use in soft decision decoding algorithms for reed solomon codes

a numerical method for the simulation of low mach number liquid gas flows this work is devoted to the numerical simulation of liquid gas flows the liquid phase is considered as incompressible while the gas phase is treated as compressible in the low mach number approximation a single fluid two pressure model is developed and the front tracking method is used to track the interface navier stokes equations coupled with that of temperature are solved in the whole computational domain velocity pressure and temperature fields are computed yielding a complete description of the dynamics for both phases we show that our method is much more efficient than the so called all mach methods involving a single pressure since large time steps can be used while retaining time accuracy the model is first validated on a reference test problem solved using an accurate ale technique to track the interface numerical examples in two space dimensions are next presented they consist of air bubbles immersed in a closed cavity filled up with liquid water the forced oscillations of the system consisting of the air bubbles and the liquid water are investigated they are driven by a heat supply or a thermodynamic pressure difference between the bubbles

efficient decoding of z sub p k linear codes we present a method for lifting a decoding scheme for a linear code over z sub p to a decoding scheme for a linear code over z sub p k and characterize the class of codes for which this kind of lifting works its interest lies in its great generality and efficiency

an immersed finite volume element method for 2d pdes with discontinuous coefficients and non homogeneous jump conditions an immersed finite volume element method is developed to solve 2d elliptic interface problems with a variable coefficient that has a finite jump across an interface the solution and the flux may also have a finite jump across the interface using the source removal technique an equivalent elliptic interface problem with homogeneous jump conditions is obtained the nodal basis functions are constructed to satisfy the homogeneous jump conditions near the interface and the usual finite element nodal basis functions are applied away from the interface the resulting linear problem is simple and easy to solve a proof of the error estimate in the energy norm is given numerical experiments demonstrate the convergence rates of the proposed method with the usual o h 2 in the l 2 the l norms and o h in the h 1 norm

runge kutta discontinuous galerkin methods for compressible two medium flow simulations one dimensional case the runge kutta discontinuous galerkin rkdg method for solving hyperbolic conservation laws is a high order finite element method which utilizes the useful features from high resolution finite volume schemes such as the exact or approximate riemann solvers tvd runge kutta time discretizations and limiters in this paper we investigate using the rkdg finite element method for compressible two medium flow simulation with conservative treatment of the moving material interfaces numerical results for both gas gas and gas water flows in one dimension are provided to demonstrate the characteristic behavior of this approach

improved list decoding of generalized reed solomon and alternant codes over galois rings we present a two stage list decoder comprising an errors only guruswami sudan gs decoder and an errors and erasures gs decoder as component decoders in the first and second stage respectively the two stages are coupled via a post processor which selects a codeword from the output list of the first component decoder from which erasure locations are obtained for the second stage when applied to a generalized reed solomon rs code over a galois ring r that maps into a generalized rs code of the same length n and minimum hamming distance d over the corresponding residue field the proposed decoder exploits the presence of zero divisors in r to correct s errors where w lceiln radic n n d 1rceil sleslceiln radic n w n d 1rceil with a probability determined by s w and the ratio of the number of nontrivial zero divisors to the number of units in the code alphabet focusing primarily on alternant codes over zopf 2l an important class of subring subcodes of generalized rs codes over gr 2l a we demonstrate that the gs decoding radius w can be exceeded by a substantial margin with significant probability

on the cancellation problem in calculating compressible low mach number flows in calculating low mach number flows one faces the stiffness problem in two different facets the applicable time steps become very small the constants of the cancellation errors become very large 1 usually the first point receives attention here we want toconcentrate on the cancellation problem only to our knowledge there is no detailed investigation of this problem in the related literature in primitive variable formulations the problem can be solved by using the pressure coefficient instead of the pressure and a similar variable for the temperature or the internal energy in conservative variable formulations this is thought not to be possible and therefore is sacrificed we are able to show that a local reference state can also be introduced into a conservative scheme if carefully applied to all quantities and applied to all constituent parts of the program a detailed error analysis is given for all these parts finally we show that we can perform a very low mach number calculation atm 10 11with a seven digits arithmetic only and still maintain the set of conservative variables the governing equations are unaltered and the method depends neither on the time integration scheme nor the specific discretization the method should be used in connection with the standard strategies like preconditioning multigrid or an semi implicit method if acceleration is desired

efficient symmetric discretization for the poisson heat and stefan type problems with robin boundary conditions we present a novel and efficient method for solving the poisson equation the heat equation and stefan type problems with robin boundary conditions over potentially moving arbitrarily shaped domains the method utilizes a level set framework thus it has all of the benefits of a sharp implicitly represented interface such as the ease of handling complex topological changes this method is straightforward to implement and leads to a linear system that is symmetric and positive definite which can be inverted efficiently with standard iterative methods this approach is second order accurate for both the poisson and heat equations and first order accurate for the stefan problem we demonstrate the accuracy in the l 1 and l norms

fast marching methods fast marching methods are numerical schemes for computing solutions to the nonlinear eikonal equation and related static hamilton jacobi equations based on entropy satisfying upwind schemes and fast sorting techniques they yield consistent accurate and highly efficient algorithms they are optimal in the sense that the computational complexity of the algorithms is o n log n where n is the total number of points in the domain the schemes are of use in a variety of applications including problems in shape offsetting computing distances from complex curves and surfaces shape from shading photolithographic development computing first arrivals in seismic travel times construction of shortest geodesics on surfaces optimal path planning around obstacles and visibility and reflection calculations in this paper we review the development of these techniques including the theoretical and numerical underpinnings provide details of the computational schemes including higher order versions and demonstrate the techniques in a collection of different areas

a robust implicitexplicit acoustic transport splitting scheme for two phase flows in this paper a splitting strategy to simulate compressible two phase flows using the five equation model is presented the main idea of the splitting is to separate the acoustic and transport phenomena the acoustic step is solved in a non conservative form using a scheme based on an approximate riemann solver since the acoustic time step induced by the fast sound velocity is very restrictive an implicit treatment of this step is performed for the transport step driven by the slow material waves an explicit scheme is used although non conservative forms are used to derive numerical schemes for the two steps the overall scheme resulting from this splitting operator strategy is conservative it preserves contact discontinuities and reveals to be very robust compared to a standard unsplit scheme numerical simulations of compressible two phase flows are presented on two dimensional structured grids the implicitexplicit strategy allows large time steps which do not depend on the fast acoustic waves

a generalized approach for sub and super critical flows using the local discontinuous galerkin method abstract we present a generalized approach to solve sub and super critical flows using the local discontinuous galerkin ldg method the 5 equation model is used to capture multiple phases this model converges to the euler equation when only one phase is present the formulation is independent of the equation of state eos in each phase and thus allows for a more accurate representation of the different fluids by using their appropriate eos the multi phase model includes the convection of the volume fraction which is modeled by a hamilton jacobi equation this appears to be the first study that demonstrates the solution of the volume fraction in a two phase model using the ldg method a modified moment limiter is used to prevent oscillations close to discontinuities and shows that limiting using primitive instead of conservative variables is significantly bigger in two phase flows when compared to a single phase flow an additional limiting technique to minimize the numerical diffusion is introduced which is shown to be especially important at the interface canonical test cases are used to verify and validate the formulation in one two and three dimensions finally the new two phase ldg approach is applied to shock bubble interaction studies and compared to available data

a level set approach to eulerian lagrangian coupling we present a numerical method for coupling an eulerian compressible flow solver with a lagrangian solver for fast transient problems involving fluid solid interactions such coupling needs arise when either specific solution methods or accuracy considerations necessitate that different and disjoint subdomains be treated with different eulerian or lagrangian schemes the algorithm we propose employs standard integration of the eulerian solution over a cartesian mesh to treat the irregular boundary cells that are generated by an arbitrary boundary on a structured grid the eulerian computational domain is augmented by a thin layer of cartesian ghost cells boundary conditions at these cells are established by enforcing conservation of mass and continuity of the stress tensor in the direction normal to the boundary the description and the kinematic constraints of the eulerian boundary rely on the unstructured lagrangian mesh the lagrangian mesh evolves concurrently driven by the traction boundary conditions imposed by the eulerian counterpart several numerical tests designed to measure the rate of convergence and accuracy of the coupling algorithm are presented as well general problems in one and two dimensions are considered including a test consisting of an isotropic elastic solid and a compressible fluid in a fully coupled setting where the exact solution is available

unified adaptive variational multiscale method for two phase compressible incompressible flows in this paper we present a new stabilized finite element method to solve the two phase compressible incompressible fluid flow problems using the level set method an anisotropic mesh adaptation with a regularized interface is adopted to deal with the high discontinuity in the material properties the coupling between the pressure and the flow velocity is ensured by introducing mass conservation terms in the momentum equation therefore the same set of primitive unknowns and equations is described for both phases the unified system is solved using a new derived variational multiscale stabilized finite element method it is tested on three time dependent liquid gas interface problems the numerical results show good stability and accuracy properties permitting also to deal with important compressibility effect high density ratio and extremely stretched anisotropic elements

a barely implicit correction for flux corrected transport abstract the barely implicit correction bic removes the stringent limit on the timestep imposed by the sound speed in explicit methods this is done by adding one elliptic equation which has to be solved implicitly bic is combined with the flux corrected transport algorithm in order to represent sharp gradients in subsonic flows accurately the resultant conservative algorithm costs about the same per timestep as a single explicit timestep calculated using an optimized fct module several examples show the technique s ability to solve nearly incompressible flows very economically

adaptive solution techniques for simulating underwater explosions and implosions adaptive solution techniques are presented for simulating underwater explosions and implosions the liquid is assumed to be an adiabatic fluid and the solution in the gas is assumed to be uniform in space the solution in water is integrated in time using a semi implicit time discretization of the adiabatic euler equations results are presented either using a non conservative semi implicit algorithm or a conservative semi implicit algorithm a semi implicit algorithm allows one to compute with relatively large time steps compared to an explicit method the interface solver is based on the coupled level set and volume of fluid method clsvof m sussman a second order coupled level set and volume of fluid method for computing growth and collapse of vapor bubbles j comput phys 187 2003 110 136 m sussman e g puckett a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows j comput phys 162 2000 301 337 several underwater explosion and implosion test cases are presented to show the performances of our proposed techniques

a projection method for low speed flows we propose a decomposition applicable to low speed inviscid flows of all mach numbers less than 1 by using the hodge decomposition we may write the velocity field as the sum of a divergence free vector field and a gradient of a scalar function evolution equations for these parts are presented a numerical procedure based on this decomposition is designed using projection methods for solving the incompressible variables and a backward euler method for solving the potential variables numerical experiments are included to illustrate various aspects of our algorithm

the ghost fluid method for compressible gas water simulation an analysis is carried out for the ghost fluid method gfm based algorithm as applied to the gas water riemann problems which can be construed as two single medium gfm riemann problems it is found that the inability to provide correct and consistent riemann waves in the respective real fluids by these two gfm riemann problems may lead to inaccurate numerical results based on this finding two conditions are suggested and imposed for the ghost fluid status in order to ensure that correct and consistent riemann waves are provided in the respective real fluids during the numerical decomposition of the singularity using these two conditions to analyse some of the existing gfm based algorithms such as the original gfm j comput phys 152 1999 457 the new version gfm j comput phys 166 2001 1 j comput phys 175 2002 200 and the modified gfm mgfm j comput phys 190 2003 651 it is found that there are ranges of conditions for each type of solution where either the original gfm or the new version gfm or both are unable to provide correct or consistent riemann waves in one of the real fluids within these ranges examples can be found such that either the original gfm or the new version gfm or both are unable to provide accurate results the mgfm is also found to encounter difficulties when applied to nearly cavitating flow various examples are presented to demonstrate the conclusions obtained the mgfm with proposed modification when applied to nearly cavitating flow is then found to be quite robust and can provide relatively reasonable results

stochastic differential equations and geometric flows in previous years curve evolution applied to a single contour or to the level sets of an image via partial differential equations has emerged as an important tool in image processing and computer vision curve evolution techniques have been utilized in problems such as image smoothing segmentation and shape analysis we give a local stochastic interpretation of the basic curve smoothing equation the so called geometric heat equation and show that this evolution amounts to a tangential diffusion movement of the particles along the contour moreover assuming that a priori information about the shapes of objects in an image is known we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise we also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features in contrast to the original geometric heat flow which tends to circularize any closed curve

regular article extension of finite volume compressible flow solvers to multi dimensional variable density zero mach number flows when attempting to compute unsteady variable density flows at very small or zero mach number using a standard finite volume compressible flow solver one faces at least the following difficulties i spatial pressure variations vanish as the mach number m 0 but they do affect the velocity field at leading order ii the resulting spatial homogeneity of the leading order pressure implies an elliptic divergence constraint for the energy flux iii violations of this constraint crucially affect the transport of mass preventing a code to properly advect even a constant density distribution we overcome these difficulties through a new algorithm for constructing numerical fluxes in the context of multi dimensional finite volume methods in conservation form the construction of numerical fluxes involves 1 an explicit upwind step yielding predictions for the nonlinear convective flux components 2 a first correction step that introduces pressure gradients which guarantee compliance of the convective fluxes with a divergence constraint this step requires the solution of a first poisson type equation 3 a second projection step which provides the yet unknown non convective pressure contribution to the total flux of momentum this second projection requires the solution of another poisson type equation and yields the cell centered velocity field at the new time this velocity field exactly satisfies a divergence constraint consistent with the asymptotic limit step 1 can be done by any standard finite volume compressible flow solver the input to steps 2 and 3 involves solely the fluxes from step 1 and is independent of how these were obtained thus our approach allows any such solver to be extended to compute variable density incompressible flows

a level set formulation of eulerian interface capturing methods for incompressible fluid flows a level set formulation is derived for incompressible immiscible navier stokes equations separated by a free surface the interface is identified as the zero level set of a smooth function eulerian finite difference methods based on this level set formulation are proposed these methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection numerical experiments are presented to demonstrate the effectiveness of the methods

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

a numerical method for two phase flow consisting of separate compressible and incompressible regions abstract we propose a numerical method for modeling two phase flow consisting of separate compressible and incompressible regions this is of interest for example when the combustion of fuel droplets or the shock induced mixing of liquids is numerically modeled we use the level set method to track the interface between the compressible and incompressible regions as well as the ghost fluid method gfm to create accurate discretizations across the interface the gfm is particularly effective here since the equations differ in both number and type across the interface the numerical method is presented in two spatial dimensions with numerical examples in both one and two spatial dimensions while three dimensional extensions are straightforward

a discontinuous galerkin finite element method for directly solving the hamilton jacobi equations in this paper we propose a new discontinuous galerkin finite element method to solve the hamilton jacobi equations unlike the discontinuous galerkin method of c hu c w shu a discontinuous galerkin finite element method for hamilton jacobi equations siam journal on scientific computing 21 1999 666 690 which applies the discontinuous galerkin framework on the conservation law system satisfied by the derivatives of the solution the method in this paper applies directly to the solution of the hamilton jacobi equations for the linear case this method is equivalent to the traditional discontinuous galerkin method for conservation laws with source terms thus stability and error estimates are straightforward for the nonlinear convex hamiltonians numerical experiments demonstrate that the method is stable and provides the optimal k 1 th order of accuracy for smooth solutions when using piecewise kth degree polynomials singularities in derivatives can also be resolved sharply if the entropy condition is not violated special treatment is needed for the entropy violating cases both one and two dimensional numerical results are provided to demonstrate the good qualities of the scheme

a simple stabilized finite element method for solving two phase compressible incompressible interface flows abstract when computing interface flows between compressible gas and incompressible liquid fluids one faces at least to the following difficulties 1 transition from a gas density linked to the local temperature and pressure by an equation of state to a liquid density mainly constant in space 2 proper approximation of the divergence constraint in incompressible regions and 3 wave transmission at the interface the aim of the present paper is to design a global i e the same for each phase numerical method to address easily this coupling to this end the same set of primitive unknowns and equations is used everywhere in the flow but with a dynamic parameterization that changes from compressible to incompressible regions on one hand the compressible navier stokes equations are considered under weakly compressibility assumption so that a non conservative formulation can be used on the other hand the incompressible non isothermal model is retained in addition the level set transport equation is used to capture the interface position needed to identify the local characteristics of the fluid and to recover the adequate local modelling for space approximation of navier stokes equations a galerkin least squares finite element method is used two essential elements for defining this numerical scheme are the stabilization and the computation of element integral of the approximated weak form since very different concerns motivate the need for stabilization in compressible and incompressible flows the first difficulty is to design a stabilization operator suitable for both types of flows especially in mixed elements in addition some integral of discontinuous functions must be correctly computed to ensure interfacial wave transmission to overcome these two difficulties specific averages are computed especially near the interface finally the level set transport equation is computed by a quadrature free discontinuous galerkin method numerical strategies are performed and validated for 1d and 2d applications

how to prevent pressure oscillations in multicomponent flow calculations a new numerical scheme for computing multicomponent flows is presented it is able to handle strong shocks is pressure oscillation free through the contact discontinuities and guarantees the posi tivity of mass fractions some numerical experiments on shock tubes indicate the convergence to the correct weak solution comparisons with classical finite volume schemes are also proposed

a semi implicit augmented iim for navier stokes equations with open traction or free boundary conditions in this paper a new navier stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open traction and free boundary conditions which can be applied to simulations of fluid structure interaction implicit solvent model for biomolecular applications and other free boundary or interface problems for some problems of this type the projection method and the augmented immersed interface method iim do not work well or does not work at all the proposed new navier stokes solver is based on the local pressure boundary method and a semi implicit augmented iim a fast poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future the time discretization is based on a second order multi step method numerical tests with exact solutions are presented to validate the accuracy of the method application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented

a boundary condition capturing method for poisson s equation on irregular domains interfaces have a variety of boundary conditions or jump conditions that need to be enforced the ghost fluid method gfm was developed to capture the boundary conditions at a contact discontinuity in the inviscid euler equations and has been extended to treat more general discontinuities such as shocks detonations and deflagrations and compressible viscous flows in this paper a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous this new method is robust and easy to implement even in three spatial dimensions furthermore the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient poisson equation in the absence of interfaces allowing for straightforward application of standard black box solvers

an interface treating technique for compressible multi medium flow with runge kutta discontinuous galerkin method the high order accurate runge kutta discontinuous galerkin rkdg method is applied to the simulation of compressible multi medium flow generalizing the interface treating method given in chertock et al 2008 9 in mixed cells where the interface is located riemann problems are solved to define the states on both sides of the interface the input states to the riemann problem are obtained by extrapolation to the cell boundary from solution polynomials in the neighbors of the mixed cell the level set equation is solved by using a high order accurate rkdg method for hamilton jacobi equations resulting in a unified dg solver for the coupled problem the method is conservative if we include the states in the mixed cells which are however not used in the updating of the numerical solution in other cells the states in the mixed cells are plotted to better evaluate the conservation errors manifested by overshoots undershoots when compared with states in neighboring cells these overshoots undershoots in mixed cells are problem dependent and change with time numerical examples show that the results of our scheme compare well with other methods for one and two dimensional problems in particular the algorithm can capture well complex flow features of the one dimensional shock entropy wave interaction problem and two dimensional shock bubble interaction problem

runge kutta discontinuous galerkin method for the approximation of baer and nunziato type multiphase models a high order numerical method is developed for the computation of compressible multiphase flows the model we use is based on the baer and nunziato type systems 4 among all the other available models in the literature these systems present the advantage to be able to simulate either interface or mixture problems nevertheless they still raise some issues mainly based on their non conservative feature the numerical method we propose is a discontinuous galerkin type in this work the interior side integrals are computed thanks to 2 robustness and high order of accuracy of the method are proved on classical interface problems but also on suitably derived analytical solutions

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

a second order boundary fitted projection method for free surface flow computations this paper describes a new approach to the high fidelity simulation of axisymmetric free surface flows a boundary fitted grid is coupled with a new projection method for the solution of the navier stokes equations with second order accuracy in space and time two variants of this new method are developed by adapting two existing algorithms suitable for prescribed velocity boundary conditions to the case of prescribed normal and tangential stresses at the free boundary a normal mode analysis for a fixed boundary problem confirms the second order accuracy of the algorithms the approach is validated by comparison with a rayleigh plesset solution for an oscillating spherical bubble with an analysis of shape oscillations and with existing results for the buoyant rise of a deforming bubble for reynolds numbers up to 200 and weber numbers up to 12 in addition to the simulation of axisymmetric free surface flows of intrinsic interest the present approach is suitable for the validation of genuinely three dimensional calculations

a riemann problem based method for solving compressible and incompressible flows a riemann problem based method for solving two medium flow including compressible and incompressible regions is presented the material interface is advanced by front tracking method and the material interface boundary conditions are defined by modified ghost fluid method a coupled compressible and incompressible riemann problem constructed in the normal direction of the material interface is proposed to predict the interfacial states with the ghost fluid states the compressible and incompressible flows are solved by discontinuous galerkin method an incompressible discontinuous galerkin method with nonuniform time step is also deduced for shock wave formed in compressible flow the numerical errors for the ghost fluid method in earlier works are analyzed and discussed in the numerical examples it shows that the proposed method can provide reasonable results including shock wave location two medium flow including compressible and incompressible regions is investigated an incompressible discontinuous galerkin method with nonuniform time step is derived a coupled compressible and incompressible riemann problem is proposed reasonable results are obtained for strong shock wave formed in compressible flow

a boundary condition capturing method for incompressible flame discontinuities abstract in this paper we propose a new numerical method for treating two phase incompressible flow where one phase is being converted into the other e g the vaporization of liquid water we consider this numerical method in the context of treating discontinuously thin flame fronts for incompressible flow this method was designed as an extension of the ghost fluid method 1999 j comput phys 152 457 and relies heavily on the boundary condition capturing technology developed in liu et al 2000 j comput phys 154 15 for the variable coefficient poisson equation and in kang et al in press j comput phys for multiphase incompressible flow our new numerical method admits a sharp interface representation similar to the method proposed in helenbrook et al 1999 j comput phys 148 366 since the interface boundary conditions are handled in a simple and straightforward fashion the code is very robust e g no special treatment is required to treat the merging of flame fronts the method is presented in three spatial dimensions with numerical examples in one two and three spatial dimensions

numerical simulation of free surface incompressible liquid flows surrounded by compressible gas a numerical model for the three dimensional simulation of liquid gas flows with free surfaces is presented the incompressible navier stokes equations are assumed to hold in the liquid domain in the gas domain the velocity is disregarded the pressure is supposed to be constant in each connected component of the gas domain and follows the ideal gas law the gas pressure is imposed as a normal force on the liquid gas interface an implicit splitting scheme is used to decouple the physical phenomena given the gas pressure on the interface the method described in j comput phys 155 1999 439 int j numer meth fluids 42 7 2003 697 is used to track the liquid domain and to compute the velocity and pressure fields in the liquid then the connected components of the gas domain are found using an original numbering algorithm finally the gas pressure is updated from the ideal gas law in each connected component of gas the implementation is validated in the frame of mould filling numerical results in two and three space dimensions show that the effect of pressure in the bubbles of gas trapped by the liquid cannot be neglected

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

list decoding of generalized reed solomon codes over commutative rings we show that the list decoding procedure of guruswami and sudan may be used to decode generalized reed solomon rs codes defined over commutative rings with identity an algorithm for performing the first of the two phases of this decoding procedure is also given in particular we show that for generalized rs codes over chain rings the probability of picking an incorrect codeword from a given list can be reduced by increasing the size of the code alphabet while keeping the length and minimum hamming distance of the code constant

computing minimal surfaces via level set curvature flow given a fixed closed curve or curves in r sp3 there is an associated problem of finding a surface with mean curvature zero which has that curve or curves as its boundary in this paper a new approach to numerically solving the minimal surface problem is introduced the surface is represented as a level set of a global function phi r sp3 to r the family of surfaces evolve in time according to mean curvature flow a solution is found when a steady state condition is achieved a new system of interpolatory boundary conditions are used to maintain the connection between the surface and the fixed boundary contour several computer surfaces are shown including examples of topological changes

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

hybrid multifluid algorithms extensions of many successful single component schemes to compute multicomponent gas dynamics suffer from oscillations and other computational inaccuracies near material interfaces that are caused by the failure of the schemes to maintain pressure equilibrium between the fluid components a new algorithm based on the compressible euler equations for multicomponent fluids augmented by the pressure evolution equation is presented the extended set of equations offers two alternative ways to update the pressure field i using the equation of state or ii using the pressure evolution equation in a numerical implementation these two procedures generally yield different answers the former is a standard conservative update but may produce oscillations near material interfaces the latter is nonconservative but becomes exact near interfaces and automatically maintains pressure equilibrium a hybrid scheme which selects from the two pressure update procedures is presented the scheme perfectly conserves total mass and momentum and conserves total energy everywhere except at a finite very small number of grid cells computed solutions exhibit oscillation free interfaces and have em negligible relative conservation errors in total energy even for very strong shocks the proposed hybrid approach and switching strategies are independent of the numerical implementation and may provide a simple framework within which to extend one s favourite scheme to solve multifluid dynamics

on generalized reed solomon codes over commutative and noncommutative rings in this paper we study generalized reed solomon codes grs codes over commutative and noncommutative rings we show that the classical welch berlekamp and guruswami sudan decoding algorithms still hold in this context and we investigate their complexities under some hypothesis the study of noncommutative grs codes over finite rings leads to the fact that grs codes over commutative rings have better parameters than their noncommutative counterparts also grs codes over finite fields have better parameters than their commutative rings counterparts but we also show that given a unique decoding algorithm for a grs code over a finite field there exists a unique decoding algorithm for a grs code over a truncated power series ring with a better asymptotic complexity moreover we generalize a lifting decoding scheme to obtain new unique and list decoding algorithms designed to work when the base ring is for example a galois ring or a truncated power series ring or the ring of square matrices over the latter ring

computation of compressible and incompressible flows with a space time stabilized finite element method abstract this paper presents the numerical results of compressible and incompressible flow problems through a unified approach based on a stabilized space time finite element method the numerical approach is continuous in space and discontinuous in time the proposed method starts by the use of a stabilized space time variational formulation which allows the use of the same order interpolation functions for all solution variables the numerical technique is tested through comparison with standard compressible and incompressible flow benchmarks compressible flow cases include 1d and 2d shock problems incompressible flow cases include lid driven cavity flow and flow over a backward facing step computed over a range of r e numbers the results demonstrate high stability and accuracy of the numerical technique over a wide range of flow regimes suggesting straightforward extension to many flow cases not yet investigated

design of a recursive shape controlling mesh generator a recursive shape controlling triangulation method is described the method is designed to produce a labelling which implies reduced fill in the solution of finite element equations assembled from such a triangulation and allows simple implementation of a nested disection algorithm for irregular domains this approach saves a substantial amount of time usually spent on discovering a suitable relabelling of the triangulation in addition the matrix of the resulting system is then endowed with a recursive doubly bordered block diagonal form this allows us to develop a recursive parallel bisection method for the solution of the system of equations

an adaptive ghost fluid finite volume method for compressible gas water simulations an adaptive ghost fluid finite volume method is developed for one and two dimensional compressible multi medium flows in this work it couples the real ghost fluid method gfm c w wang t g liu b c khoo a real ghost fluid method for the simulation of multi medium compressible flow siam j sci comput 28 2006 278 302 and the adaptive moving mesh method h z tang t tang moving mesh methods for one and two dimensional hyperbolic conservation laws siam j numer anal 41 2003 487 515 h z tang t tang p w zhang an adaptive mesh redistribution method for non linear hamilton jacobi equations in two and three dimensions j comput phys 188 2003 543 572 and thus combines their advantages this work shows that the local mesh clustering in the vicinity of the material interface can effectively reduce both numerical and conservative errors caused by the gfm around the material interface and other discontinuities besides the improvement of flow field resolution the adaptive gfm also largely increases the computational efficiency several numerical experiments are conducted to demonstrate robustness and efficiency of the current method they include several 1d and 2d gas water flow problems involving a large density gradient at the material interface and strong shock interface interactions the results show that our algorithm can capture the shock waves and the material interface accurately and is stable and robust even for solutions with large density and pressure gradients

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data

regular article a computational model for suspended large rigid bodies in 3d unsteady viscous flows a 3d numerical model for computing large rigid objects suspended in fluid flow has been developed rather than calculating the surface pressure upon the solid body we evaluate the net force and torque based on a volume force formulation the total effective force is obtained by summing up the forces at the eulerian grids occupied by the rigid body the effects of the moving bodies are coupled to the fluid flow by imposing the velocity field of the bodies to the fluid a poisson equation is used to compute the pressure over the whole domain the objects are identified by color functions and calculated by the ppm scheme and a tangent function transformation which scales the transition region of the computed interface to a compact thickness the model is then implemented on a parallel computer of distributed memory and validated with stokes and low reynolds number flows

a hybrid particle level set method for improved interface capturing in this paper we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field our method uses lagrangian marker particles to rebuild the level set in regions which are underresolved this is often the case for flows undergoing stretching and tearing the overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method our method compares favorably with volume of fluid methods in the conservation of mass and purely lagrangian schemes for interface resolution the method is presented in three spatial dimensions