adaptive unstructured volume remeshing ii application to two and three dimensional level set simulations of multiphase flow in part i adaptive unstructured volume remeshing i the method j comput phys in press we presented an adaptive remeshing algorithm that automatically adjusts the size of the elements of meshes of unstructured triangles 2d and unstructured tetrahedra 3d with time and position in the computational domain in order to efficiently resolve the relevant physical scales here we illustrate the performance of an implementation of the algorithm in finite element level set simulations of deformable droplet and fluid fluid interface interactions breakup and coalescence in multiphase flows the wide range of length scales characterizing the dynamics are accurately resolved as demonstrated by comparison to experiments and to theoretical and sharp interface boundary integral numerical results the computational cost is found to be competitive even with respect to boundary integral methods for the first time using an interface capturing level set method we successfully simulate the inertia driven impact and rebound of a liquid droplet from a liquid interface and find agreement with recent experimental results

computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods the numerical simulation of the deformation of vesicle membranes under simple shear external fluid flow is considered in this paper a saddle point approach is proposed for the imposition of the fluid incompressibility and the membrane inextensibility constraints through lagrange multipliers defined in the fluid and on the membrane respectively using a level set formulation the problem is approximated by mixed finite elements combined with an automatic adaptive mesh procedure at the vicinity of the membrane boundary numerical experiments show that this combination of the saddle point and adaptive mesh method enhances the robustness of the method the effect of inertia on the stability of the vesicle in a shear flow is also investigated

accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

algorithm for direct numerical simulation of emulsion flow through a granular material a multipole accelerated 3d boundary integral algorithm capable of modelling an emulsion flow through a granular material by direct multiparticle multidrop simulations in a periodic box is developed and tested the particles form a random arrangement at high volume fraction rigidly held in space including the case of an equilibrium packing in mechanical contact deformable drops with non deformed diameter comparable with the particle size squeeze between the particles under a specified average pressure gradient the algorithm includes recent boundary integral desingularization tools especially important for drop solid and drop drop interactions the hebeker representation for solid particle contributions and unstructured surface triangulations with fixed topology multipole acceleration with two levels of mesh node decomposition entire drop solid surfaces and patches is a significant improvement over schemes used in previous purely multidrop simulations it remains efficient at very high resolutions 10 4 10 5 triangular elements per surface and has no lower limitation on the number of particles or drops such resolutions are necessary in the problem to alleviate lubrication difficulties especially for near critical squeezing conditions as well as using 10 4 time steps and an iterative solution at each step both for contrast and matching viscosities examples are shown for squeezing of 25 40 drops through an array of 9 14 solids with the total volume fraction of 70 for particles and drops the flow rates for the drop and continuous phases are calculated extensive convergence testing with respect to program parameters triangulation multipole truncation etc is made

multiple description coding using pairwise correlating transforms the objective of multiple description coding mdc is to encode a source into multiple bitstreams supporting multiple quality levels of decoding in this paper we only consider the two description case where the requirement is that a high quality reconstruction should be decodable from the two bitstreams together while lower but still acceptable quality reconstructions should be decodable from either of the two individual bitstreams this paper describes techniques for meeting mdc objectives in the framework of standard transform based image coding through the design of pairwise correlating transforms the correlation introduced by the transform helps to reduce the distortion when only a single description is received but it also increases the bit rate beyond that prescribed by the rate distortion function of the source we analyze the relation between the redundancy i e the extra bit rate and the single description distortion using this transform based framework we also describe an image coder that incorporates the pairwise transform and show its redundancy rate distortion performance for real images

oversampled filter banks from extended perfect reconstruction filter banks oversampled filter banks are currently being proposed for robust transmission applications in this paper we completely characterize multidimensional doubly finite impulse response fir filter banks that is oversampled filter banks whose dual is fir then we consider the problem of extending perfect reconstruction critically sampled multidimensional filter banks in order to obtain doubly fir dfir filter banks as a result very simple criteria for constructing dfir filter banks as extensions of orthogonal filter banks are obtained this paper also analyzes the problem of constructing totally fir filter banks i e dfir filter banks that remain dfir even when some channels are removed it is shown that any totally fir filter bank can be implemented as the cascade of a critically sampled dfir filter bank whose number of channels is equal to the subsampling factor a redundant finite dimensional transform and a suitable set of delays

computation of the para pseudoinverse for oversampled filter banks forward and backward greville formulas frames and oversampled filter banks have been extensively studied over the past few years due to their increased design freedom and improved error resilience in frame expansions the least square signal reconstruction operator is called the dual frame which can be obtained by choosing the synthesis filter bank as the para pseudoinverse of the analysis bank in this paper we study the computation of the dual frame by exploiting the greville formula which was originally derived in 1960 to compute the pseudoinverse of a matrix when a new row is appended here we first develop the backward greville formula to handle the case of row deletion based on the forward greville formula we then study the computation of para pseudoinverse for extended filter banks and laplacian pyramids through the backward greville formula we investigate the frame based error resilient transmission over erasure channels the necessary and sufficient condition for an oversampled filter bank to be robust to one erasure channel is derived a postfiltering structure is also presented to implement the para pseudoinverse when the transform coefficients in one subband are completely lost

simulations of multiphase flows with multiple length scales using moving mesh interface tracking with adaptive meshing in multiphase flows the length scales of thin regions such as thin films between nearly touching drops and thin threads formed during the interface pinch off are usually several orders of magnitude smaller than the size of the drops in this paper a number of extra length criteria for adaptive meshes are developed and implemented in the moving mesh interface tracking method to solve these multiple length scale problems with high fidelity a nominal length scale based on the solutions of laplace s equations with the unit normal vectors of surfaces as the boundary conditions is proposed for the adaptive mesh refinement in the thin regions for almost flat interfaces boundaries which are near to the thin regions the averaged length of the interior edges sharing the two nodes with the boundary edge is introduced for the mesh adaptation the averaged length of the interfacial edges is used for the interior elements near the interfaces but outside of the thin regions for the interior mesh away from the interfaces boundaries different averaged length scales based on the initial mesh are employed for the adaptive mesh refining and coarsening numerous cases are simulated to demonstrate the capability of the proposed schemes in handling multiple length scales which include the relaxation and necking of an elongated droplet droplet droplet head on approaching droplet wall interactions and a droplet pair in a shear flow the smallest length resolved for the thin regions is three orders of magnitude smaller than the largest characteristic length of the problem

burst erasures and the mean square error for cyclic parseval frames this paper investigates the performance of frames for the linear redundant encoding of vectors when consecutive frame coefficients are lost due to the occurrence of random burst errors we assume that the distribution of bursts is invariant under cyclic shifts and that the burst length statistics are known in analogy with rate distortion theory we wish to find frames of a given size which minimize the mean square reconstruction error for the encoding of vectors in a complex finite dimensional hilbert space we obtain an upper bound for the mean square reconstruction error for a given parseval frame and in the case of cyclic parseval frames we find a family of frames which minimizes this upper bound under certain conditions these minimizers are identical to complex bose chaudhuri hocquenghem codes discussed in the literature the accuracy of our upper bounds for the mean square error is substantiated by complementary lower bounds all estimates are based on convexity arguments and a discrete rearrangement inequality

phase field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing this paper describes a novel numerical algorithm for simulating interfacial dynamics of non newtonian fluids the interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously the property and evolution of the interfacial layer is governed by a phase field variable that obeys a cahn hilliard type of convection diffusion equation this circumvents the task of directly tracking the interface and produces the correct interfacial tension from the free energy stored in the mixing layer viscoelasticity and other types of constitutive equations can be incorporated easily into the variational phase field framework the greatest challenge of this approach is in resolving the sharp gradients at the interface this is achieved by using an efficient adaptive meshing scheme governed by the phase field variable the finite element scheme easily accommodates complex flow geometry and the adaptive meshing makes it possible to simulate large scale two phase systems of complex fluids in two dimensional and axisymmetric three dimensional implementations the numerical toolkit is applied here to drop deformation in shear and elongational flows rise of drops and retraction of drops and torii some of these solutions serve as validation of the method and illustrate its key features while others explore novel physics of viscoelasticity in the deformation and evolution of interfaces

on error estimates of the projection methods for the navier stokes equations second order schemes we present in this paper a rigorous error analysis of several projection schemes for the approximation of the unsteady incompressible navier stokes equations the error analysis is accomplished by interpreting the respective projection schemes as second order time discretizations of a perturbed system which approximates the navier stokes equations numerical results in agreement with the error analysis are also presented

a gradient augmented level set method for unstructured grids we present and test a gradient augmented level set method for unstructured grids which has been designed to allow for easy integration in parallel flow solvers the means to this end is a hermite formulation where the gradient is stored and advected as an independent variable along with the level set function the method uses narrow band storage in conjunction with a fast marching method which is also designed to take advantage of the gradient augmentation we demonstrate through standard passive advection test cases that the proposed method is able to compute interface motion with performance comparable to popular high performing methods on structured grids

frame theoretic analysis of robust filter bank frames to quantization and erasures this paper presents the theoretic analysis for the robustness of filter bank fb frames in infinite dimensional hilbert space l2 bbz to quantization and erasures as well as studies the design of such robust frames from the perspective of both frame and fb theory first a characterization of the eigenstructure for the frame operator and the induced gram matrix of general fb frames is presented the robustness of fb frames to erasures is investigated in detail especially on the necessary and sufficient condition maximally robust frames are further analyzed by explicitly constructive methods moreover the stability and even the possible fir reconstruction of the subframe by the pseudoinverse are studied thoroughly next we examine the optimal quantized fb frames introducing a novel notion named as frame energy the universal optimality of tight fb frames to quantization is established in contrast to the optimality of only equal norm tight frames shown in previous works the added design freedom obtained by removing the equal norm constraint is explained and illustrated with examples finally the effect of erasures on the quantized fb frames is studied by incorporating the probability of erasures which shows the universal optimality of uniform tight fb frames for one erasure the optimal fb frame is usually not of equal norm and actually its norm distribution follows the reverse waterfilling principle an example of two state erasure channel model is shown to further explain our result followed by an analysis of the successive reconstruction which shows its potential application to frame based multiple description coding

kapteyn series arising in radiation problems in discussing radiation from multiple point charges or magnetic dipoles moving in circles or ellipses a variety of kapteyn series of the second kind arises some of the series have been known in closed form for a hundred years or more others appear not to be available to analytic persuasion this paper shows how 12 such generic series can be developed to produce either closed analytic expressions or integrals that are not analytically tractable in addition the method presented here may be of benefit when one has other kapteyn series of the second kind to consider thereby providing an additional reason to consider such series anew

optimal subband filter banks for multiple description coding multiple description coding refers to the encoding of an information source into multiple bit streams in a manner that each bit stream independently represents a coarse description of the source while multiple descriptions jointly convey a higher fidelity source representation thus multiple description coding allows enhanced resilience to loss of individual descriptions and can be viewed as a form of source based diversity coding this paper addresses the design of subband filter banks to optimize the rate distortion performance of multiple description subband coding the problem is formulated in a lagrangian optimization framework and is solved directly in the frequency domain to produce the optimal filter spectral responses by varying the lagrangian parameter our design obtains all points on the redundancy distortion curve for gaussian wide sense stationary input processes we consider the cases of both orthonormal and more general biorthogonal filter banks we also analyze the connections between these two solutions and quantify the gap in their optimal performance application of the proposed methods to the popular first order autoregressive ar 1 model yields very interesting and insightful results in the two extreme cases of maximum and minimum redundancy our solutions degenerate to previously known results finally comparisons with popularly deployed filter banks reveal large gaps from the theoretical performance bound

probabilistic bounds on error amplification of randomly generated frames hilbert space frames have recently attracted attention in the signal processing community in this paper we consider the problem of describing the statistical distribution of the error amplification and lower bound of a frame obtained by randomly picking vectors from a larger frame the frame pool the key result of this paper is an analytic bound to the probability of having an error amplification larger than a given value we also consider the possibility of content reconstruction using an approximate but efficient algorithm the theoretical results are completed by means of numerical experiments

new finite element finite volume level set formulation for modelling two phase incompressible flows we present a new level set method for modelling two phase incompressible flows with moving interface boundaries the method is based on a finite element fe treatment of the equations governing the motion of the interface separating two immiscible phases and a finite volume fv description of the fluid flow equations the performance of the method is demonstrated and validated using several sample problems involving two phase isothermal flows with density ratios of the order of 102 103 and viscosity ratios as high as 7 104 surface tension effects are included the present formulation displays good convergence properties and it is relatively simple to program this allows the method to be implemented into existing commercial fv based computational fluid dynamics cfd software thereby extending their application range we have successfully implemented the method in the code cfx 4

local remeshing for large amplitude grid deformations fluid structure interaction fsi modelling can involve large deformations in the fluid domain which could lead to degenerating mesh quality and numerical inaccuracies or instabilities if allowed to amplify unchecked complete remeshing of the entire domain during the solution process is computationally expensive and can require interpolation of solution variables between meshes as an alternative we investigate a local remeshing algorithm with two emphases a the identification and remedy of flat degenerate tetrahedra and b the avoidance of node motion and hence associated interpolation errors initially possible topological changes are examined using a dynamic programming algorithm to maximise the minimum local element quality through edge reconnection in the 3d situation it was found that reconnection improvements tend to be limited to long edges and those with few three or four element neighbours the remaining degenerate elements are classified into one of four types using three proposed metrics the minimum edge to edge distance ee the minimum node to edge distance ne and the shortest edge length se and removed according to the best manner for their type optimised thresholds for identifying and classifying elements for removal were found to be ee 0 18 ne 0 21 se 0 2

accurate representation of surface tension using the level contour reconstruction method some of the most demanding tests of interface methods for two phase flows with surface tension which use fixed eulerian grids occur at the two extremes of highly dynamic flows or static equilibrium conditions it has been difficult to design an interface method to operate accurately across this spectrum especially for 3d fluid flow calculations which on the one hand do not often have the required grid resolution to capture all of the fine scale structures that typically appear in highly stretched interfaces nor on the other hand the required accuracy in calculating surface tension forces we present improvements to the interface reconstruction procedure in the level contour reconstruction method lcrm j comput phys 180 2002 427 which now allow the reconstruction to proceed using a locally instead of a globally calculated contour value these improvements allow more precise control of the interface reconstruction in highly dynamic flows with coalescence and rupture and also avoid the problem of local mass redistribution in poorly resolved calculations in addition a new hybrid technique for surface tension calculation in the context of the front tracking method is demonstrated and shown to result in a marked improvement in suppressing parasitic currents by generally two orders of magnitude we compare and validate these new procedures in various test cases

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

a new coupling strategy for fluid solid interaction problems by using the interface element method this paper presents a new approach to simulate fluid solid interaction fsi problems involving non matching meshes the coupling between the fluid and solid domains with dissimilar finite element meshes consisting of 4 node quadrilateral elements is achieved by using the interface element method continuity and compatibility conditions across the interface between fluid and solid meshes are satisfied exactly by introducing the interface elements defined on an interfacing region importantly a consistent transfer of loads through the interface elements guarantees the present method to be an efficient approach of the solution strategy to fsi problems an arbitrary lagrangian eulerian description is adopted for the fluid domain while for the solid domain an updated lagrangian formulation is considered to accommodate finite deformations of an elastic structure the fluid equations for velocity and pressure and the solid equations for velocity are strongly coupled in a single computational domain by means of the interface elements numerical results are presented for fsi problems involving non matching meshes to demonstrate the effectiveness of the methodology copyright 2009 john wiley sons ltd

resolving the shock induced combustion by an adaptive mesh redistribution method an adaptive mesh method is presented for numerical simulation of shock induced combustion the method is composed of two independent ingredients a flow solver and a mesh redistribution algorithm the flow solver is a finite volume based second order upwind tvd scheme together with a lower upper symmetric gauss seidel relaxation scheme for solving the multispecies navier stokes equations with finite rate chemistry the adaptive mesh is determined by a grid generation method based on solving poisson equations with the monitor function carefully designed to resolve both sharp fronts and the induction zone between them numerically it is found that the resolution of the induction zone is particularly critical to the combustion problems and an under resolved numerical method may cause excessive energy release and spurious runaway reactions the monitor function proposed in this paper which is based on the relative rate of change of mass fraction covered this issue satisfactorily numerical simulations of supersonic flows past an axisymmetric projectile in a premixed hydrogen oxygen or air mixture are carried out the results show that the spurious runaway chemical reactions appearing on coarse grids can be eliminated by using adaptive meshes without invoking any ad hoc treatment for reaction rates the adaptive mesh approach is more effective than the fixed mesh one in obtaining grid independent results finally discrepancies between the numerical and benchmark experimental results and difficulties in simulating the detonation waves are delineated which appeal for further investigation

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

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

an adaptive mesh algorithm for evolving surfaces simulation of drop breakup and coalescence abstract an algorithm is presented for the adaptive restructuring of meshes on evolving surfaces the resolution of the relevant local length scale is maintained everywhere with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations the resulting discretization depends on the instantaneous configuration of the surface but is insensitive to the deformation history application of the adaptive discretization algorithm is illustrated with three dimensional boundary integral simulations of deformable drops in stokes flow the results show that the algorithm can accurately resolve detailed features of deformed fluid interfaces including slender filaments associated with drop breakup and dimpled regions associated with drop coalescence our algorithm should be useful in a variety of fields including computational fluid dynamics image processing geographical information systems and biomedical engineering problems

integral representation of first kind kapteyn series the main aim of this research note is to establish two different types of integral representation formulae for the kapteyn series of the first kind the first one is a double definite integral expression while the second type includes indefinite integral representation formula

a balanced force refined level set grid method for two phase flows on unstructured flow solver grids a balanced force refined level set grid method for two phase flows on structured and unstructured flow solver grids is presented to accurately track the phase interface location an auxiliary high resolution equidistant cartesian grid is introduced in conjunction with a dual layer narrow band approach this refined level set grid method allows for parallel efficient grid convergence and error estimation studies of the interface tracking method the navier stokes equations are solved on an unstructured flow solver grid with a novel balanced force algorithm for level set methods based on the recently proposed method by francois et al m m francois s j cummins e d dendy d b kothe j m sicilian m w williams a balanced force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework j comput phys 213 2006 141 173 for volume of fluid methods on structured grids to minimize spurious currents a second order converging curvature evaluation technique for level set methods is presented the results of several different test cases demonstrate the effectiveness of the proposed method showing good mass conservation properties and second order converging spurious current magnitudes

an adaptive coupled level set volume of fluid interface capturing method for unstructured triangular grids we present an adaptive coupled level set volume of fluid aclsvof method for interfacial flow simulations on unstructured triangular grids at each time step we evolve both the level set function and the volume fraction the level set function is evolved by solving the level set advection equation using a discontinuous galerkin finite element method the volume fraction advection is performed using a lagrangian eulerian method the interface is reconstructed based on both the level set and the volume fraction information in particular the interface normal vector is calculated from the level set function while the line constant is determined by enforcing mass conservation based on the volume fraction different from previous works we have developed an analytic method for finding the line constant on triangular grids which makes interface reconstruction efficient and conserves volume of fluid exactly the level set function is finally reinitialized to the signed distance to the reconstructed interface since the level set function is continuous the normal vector calculation is easy and accurate compared to a classic volume of fluid method while tracking the volume fraction is essential for enforcing mass conservation the method is also coupled to a finite element based stokes flow solver the code validation shows that our method is second order and mass is conserved very accurately in addition owing to the adaptive grid algorithm we can resolve complex interface changes and interfaces of high curvature efficiently and accurately

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

on the approximation of the unsteady navier stokes equations by finite element projection methods this paper provides an analysis of a fractional step projection method to compute incompressible viscous flows by means of finite element approximations the analysis is based on the idea that the appropriate functional setting for projection methods must accommodate two different spaces for representing the velocity fields calculated respectively in the viscous and the incompressible half steps of the method such a theoretical distinction leads to a finite element projection method with a poisson equation for the incremental pressure unknown and to a very practical implementation of the method with only the intermediate velocity appearing in the numerical algorithm error estimates in finite time are given an extension of the method to a problem with unconventional boundary conditions is also considered to illustrate the flexibility of the proposed method

efficient reconstruction from frame based multiple descriptions redundant bases or frames are a promising technique for multiple description signal coding frames can provide sufficient redundancy for recovery in case of coefficient losses due for instance to packet transmission errors in this paper we consider the problem of dual frame computation in the context of finite impulse response fir analysis and synthesis filterbanks in particular we propose an algorithm for dual frame computation which recovers the missing frame coefficients followed by synthesis with the original filterbank it is shown that the algorithm operates locally and allows for reduced complexity and low delay reconstruction of the original signal the case of excessive losses and incomplete bases is also considered experiments are provided to evaluate the algorithm performance and test its applicability in practical contexts

causal compensation for erasures in frame representations in a variety of signal processing and communications contexts erasures occur inadvertently or can be intentionally introduced as part of a data reduction strategy this paper discusses causal compensation for erasures in frame representations of signals the approach described assumes linear synthesis of the signal using a prespecified frame but no specific generation mechanism for the coefficients under this assumption it is demonstrated that erasures can be compensated for using low complexity causal systems if the transmitter is aware of the occurrence of the erasure an optimal compensation is to project the erasure error to the remaining coefficients it is demonstrated that the same compensation can be executed using a transmitter receiver combination in which the transmitter is not aware of the erasure occurrence the transmitter precompensates using projections as if assuming erasures will occur the receiver undoes the compensation for the coefficients that have not been erased thus maintaining the compensation only of the erased coefficients the stability of the resulting systems is explored and stability conditions are derived it is shown that stability for any erasure pattern can be enforced by optimizing a constrained quadratic program at the system design stage the paper concludes with examples and simulations that verify the theoretical results and illustrate key issues in the algorithms

prost a parabolic reconstruction of surface tension for the volume of fluid method volume of fluid vof methods are popular for the direct numerical simulation of time dependent viscous incompressible flow of multiple liquids as in any numerical method however it has its weaknesses namely for flows in which the capillary force is the dominant physical mechanism the lack of convergence with spatial refinement or convergence to a solution that is slightly different from the exact solution has been documented in the literature a well known limiting case for this is the existence of spurious currents for the simulation of a spherical drop with zero initial velocity these currents are present in all previous versions of vof algorithms in this paper we develop an accurate representation of the body force due to surface tension which effectively eliminates spurious currents we call this algorithm prost parabolic reconstruction of surface tension there are several components to this procedure including the new body force algorithm improvements in the projection method for the navier stokes solver and a higher order interface advection scheme the curvature to the interface is calculated from an optimal fit for a quadratic approximation to the interface over groups of cells

an adaptive level set approach for incompressible two phase flows we present a numerical method using the level set approach for solving incompressible two phase flow with surface tension in the level set approach the free surface is represented as the zero level set of a smooth function this has the effect of replacing the advection of density which has steep gradients at the free surface with the advection of the level set function which is smooth in addition the free surface can merge or break up with no special treatment we maintain the level set function as the signed distance from the free surface in order to accurately compute flows with high density ratios and stiff surface tension effects in this work we couple the level set scheme to an adaptive projection method for the incompressible navier stokes equations in order to achieve higher resolution of the free surface with a minimum of additional expense we present two dimensional axisymmetric and fully three dimensional results of air bubble and water drop computations

a procedure to adapt filter banks to finite length signals in this paper we consider the problem of processing finite length signals by means of critically sampled or oversampled filter banks based on a polyphase matrix factorization of the filter bank we propose a realization adaptation that does not make any assumption about the signal values outside the support of the input signal contrary to what is done for instance when using zero padding periodic repetition or extension by symmetry the proposed procedure has several advantages in particular we show that it preserves the perfect reconstruction and the general properties of the filter bank

generalized multiple description coding with correlating transforms multiple description md coding is source coding in which several descriptions of the source are produced such that various reconstruction qualities are obtained from different subsets of the descriptions unlike multiresolution or layered source coding there is no hierarchy of descriptions thus md coding is suitable for packet erasure channels or networks without priority provisions generalizing work by orchard wang vaishampayan and reibman see proc ieee int conf image processing vol i santa barbara ca p 608 11 1997 a transform based approach is developed for producing m descriptions of an n tuple source m spl les n the descriptions are sets of transform coefficients and the transform coefficients of different descriptions are correlated so that missing coefficients can be estimated several transform optimization results are presented for memoryless gaussian sources including a complete solution of the n 2 m 2 case with arbitrary weighting of the descriptions the technique is effective only when independent components of the source have differing variances numerical studies show that this method performs well at low redundancies as compared to uniform md scalar quantization

ailu preconditioning for the finite element formulation of the incompressible navier stokes equations abstract in this paper the effect of a variable reordering method on the performance of adapted incomplete lu ailu preconditioners applied to the p2p1 mixed finite element discretization of the three dimensional unsteady incompressible navier stokes equations has been studied through numerical experiments where eigenvalue distribution and convergence histories are examined it has been revealed that the performance of an ailu preconditioner is improved by adopting a variable reordering method which minimizes the bandwidth of a globally assembled saddle point type matrix furthermore variants of the existing ailu 1 preconditioner have been suggested and tested for some three dimensional flow problems it is observed that the ailu 2 outperforms the existing ailu 1 with a little extra computing time and memory

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

a stabilized finite element method using a discontinuous level set approach for the computation of bubble dynamics a novel numerical method for solving three dimensional two phase flow problems is presented this method combines a quadrature free discontinuous galerkin method for the level set equation with a pressure stabilized finite element method for the navier stokes equations the main challenge in the computation of such flows is the accurate evaluation of surface tension forces this involves the computation of the curvature of the fluid interface in the context of the discontinuous galerkin method we show that the use of a curvature computed by means of a direct derivation of the level set function leads to inaccurate and oscillatory results a more robust second order least squares computation of the curvature that filters out the high frequencies and produces converged results is presented this whole numerical technology allows to simulate a wide range of flow regimes with large density ratios to accurately capture the shape of the deforming interface of the bubble and to maintain good mass conservation

efficient visualization of high order finite elements a general method for the post processing treatment of high order finite element fields is presented the method applies to general polynomial fields including discontinuous finite element fields the technique uses error estimation and h refinement to provide an optimal visualization grid some filtering is added to the algorithm in order to focus the refinement on a visualization plane or on the computation of one single iso zero surface 2d and 3d examples are provided that illustrate the power of the technique in addition schemes and algorithms that are discussed in the paper are readily available as part of an open source project that is developed by the authors namely gmsh

numerical simulation of drop impact on a liquid liquid interface with a multiple marker front capturing method the gravity driven motion of a droplet impacting on a liquid liquid interface is studied the full navier stokes equations are solved on a fixed uniform grid using a finite difference front capturing method for the representation of fluid fluid interfaces a coupled level set volume of fluid method m sussman e g puckett a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows j comp phys 162 2000 301 337 is used in which we introduce the novel approach of describing separate interfaces with different marker functions as a consequence we prevent numerical coalescence of the droplet and the liquid liquid interface without excessive local grid refinement to validate our method numerical simulations of the drop impact event are compared with experiments z mohamed kassim e k longmire drop impact on a liquid liquid interface phys fluids 15 2003 3263 3273 furthermore a comparison is made with the numerical results of a esmaeeli g tryggvason direct numerical simulations of bubbly flows part 2 moderate reynolds number arrays j fluid mech 385 1999 325 358 for an array of rising bubbles the investigation shows that the multiple marker approach successfully prevents numerical coalescence of interfaces and adequately captures the effect of surface tension

volume of fluid interface tracking with smoothed surface stress methods for three dimensional flows motivated by the need for three dimensional methods for interface calculations that can deal with topology changes we describe a numerical scheme built from a volume of fluid interface tracking technique that uses a piecewise linear interface calculation in each cell momentum balance is computed using explicit finite volume finite differences on a regular cubic grid surface tension is implemented by the continuous surface stress or continuous surface force method examples and verifications of the method are given by comparing simulations to analytical results and experiments for sedimenting droplet arrays and capillary waves at finite reynolds number in the case of a pinching pendant drop both three dimensional and axisymmetric simulations are compared to experiments agreement is found both before and after the reconnections

transient adaptivity applied to two phase incompressible flows an anisotropic adaptation process is applied to a three dimensional incompressible two phase flow solver the solver uses a level set finite element method on unstructured tetrahedral meshes we show how the level set function can be used to build an anisotropic mesh with good properties some computations with a strong transient character and large densities ratios 1 1000 are presented we show that the efficiency of the computations can be deeply enhanced by mesh adaptations

a high order and interface preserving discontinuous galerkin method for level set reinitialization abstract a high order numerical method for interface preserving level set reinitialization is presented in this paper in the interface cells the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved in the non interface cells we compute the gradient of the level set function by solving a hamilton jacobi equation as a conservation law system using the discontinuous galerkin method following the work by hu and shu siam j sci comput 21 1999 660 690 the missing constant is then recovered by the continuity of the level set function while taking into account the characteristics to handle highly distorted initial conditions we develop a hybrid numerical flux that combines the lax friedrichs flux and the penalty flux our method is stable for non trivial test cases and handles singularities away from the interface very well when derivative singularities are present on the interface a second derivative limiter is designed to suppress the oscillations at least n 1 th order accuracy in the interface cells and nth order in the whole domain are observed for smooth solutions when nth degree polynomials are used two dimensional test cases are presented to demonstrate superior properties such as accuracy long term stability interface preserving capability and easy treatment of contact lines we also show some preliminary results on the pinch off process of a pendant drop where topological changes of the fluid interface are involved our method is readily extendable to three dimensions and adaptive meshes

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

an arbitrary lagrangian eulerian method for three phase flows with triple junction points we present a moving mesh method suitable for solving two dimensional and axisymmetric three liquid flows with triple junction points this method employs a body fitted unstructured mesh where the interfaces between liquids are lines of the mesh system and the triple junction points if exist are mesh nodes to enhance the accuracy and the efficiency of the method the mesh is constantly adapted to the evolution of the interfaces by refining and coarsening the mesh locally dynamic boundary conditions on interfaces in particular the triple points are therefore incorporated naturally and accurately in a finite element formulation in order to allow pressure discontinuity across interfaces double values of pressure are necessary for interface nodes and triple values of pressure on triple junction points the resulting non linear system of mass and momentum conservation is then solved by an uzawa method with the zero resultant condition on triple points reinforced at each time step the method is used to investigate the rising of a liquid drop with an attached bubble in a lighter liquid

instantaneous erasures in oversampled filter banks conditions for output perfect reconstruction in this paper we aim at finding the conditions that an oversampled filter bank ofb should satisfy in order to maintain its perfect reconstruction property when erasures happen in the subband domain this problem has been addressed before mainly from frame theoretic point of view and only for the case of what we call in this paper classic erasure in the frame theoretic approach the stable filter banks are associated with frames in l2 bbz and a subband erasure is defined as the deletion of the frame expansion coefficients corresponding to the frame vectors resulting from each filter and all its translated versions this is equivalent to assuming that all the samples of a subband have been completely lost classic erasure and this is why in this approach it is always assumed that each channel is either working perfectly or not at all in this paper we extend this notion of erasure to a situation where subband channels are allowed to be on or off arbitrarily in each time instance and we define a new type of erasure called instantaneous erasure using an approach based on the time domain analysis of perfect reconstruction property we introduce general conditions for perfect reconstruction of the output and also the sufficient conditions for two classes of filter banks causal ofbs with causal inverse and ofbs with maximum robustness against classic erasure

high resolution flux based level set method a new high resolution flux based finite volume method for general advection equations in nondivergent form including a level set equation for moving interfaces is introduced the method is applicable to the case of nondivergence free velocity and to general unstructured grids in higher dimensions we show that the method is consistent and that the numerical solution fulfills the discrete minimum maximum principle numerical experiments show its second order accuracy for smooth solutions as well as for solutions with discontinuous derivatives and on general unstructured meshes numerical examples for passive transport and shrinking of dynamic interfaces including examples with topological changes are presented using locally adapted two dimensional and three dimensional grids

on taylor series and kapteyn series of the first and second type abstract we study the relation between the coefficients of taylor series and kapteyn series representing the same function we compute explicit formulas for expressing one in terms of the other and give examples to illustrate our method

filter bank frame expansions with erasures we study frames for robust transmission over the internet in our previous work we used quantized finite dimensional frames to achieve resilience to packet losses here we allow the input to be a sequence in l sub 2 z and focus on a filter bank implementation of the system we present results in parallel r sup n or c sup n versus l sub 2 z and show that uniform tight frames as well as newly introduced strongly uniform tight frames provide the best performance

multiple description vector quantization with lattice codebooks design and analysis the problem of designing a multiple description vector quantizer with lattice codebook spl lambda is considered a general solution is given to a labeling problem which plays a crucial role in the design of such quantizers numerical performance results are obtained for quantizers based on the lattices a sub 2 and z sup i i 1 2 4 8 that make use of this labeling algorithm the high rate squared error distortions for this family of l dimensional vector quantizers are then analyzed for a memoryless source with probability density function pdf p and differential entropy h p spl infin for any a spl epsiv 0 1 and rate pair r r it is shown that the two channel distortion d sub o and the channel 1 or channel 2 distortion d sub s satisfy lim sub r spl rarr spl infin d sub o 2 sup 2r 1 a 1 4 g spl lambda 2 sup 2h p and lim sub r spl rarr spl infin d sub s 2 sup 2r 1 a g s sub l 2 sup 2h p where g spl lambda is the normalized second moment of a voronoi cell of the lattice spl lambda and g s sub l is the normalized second moment of a sphere in l dimensions

an efficient interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow in sussman smereka and osher j comp phys 94 1994 pp 146 159 a numerical scheme was presented for computing incompressible air water flows using the level set method crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set in this paper we implement a constraint along with higher order difference schemes in order to make the iteration method more accurate and efficient accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set we apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost we validate our results with experiment and theory we show that our distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface we perform basic accuracy checks and more stringent tests involving complicated interfacial structures as with all level set schemes our method is easy to implement

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

multiple description image coding based on lagrangian rate allocation in this paper a novel multiple description coding technique is proposed based on optimal lagrangian rate allocation the method assumes the coded data consists of independently coded blocks initially all the blocks are coded at two different rates then blocks are split into two subsets with similar rate distortion characteristics two balanced descriptions are generated by combining code blocks belonging to the two subsets encoded at opposite rates a theoretical analysis of the approach is carried out and the optimal rate distortion conditions are worked out the method is successfully applied to the jpeg 2000 standard and simulation results show a noticeable performance improvement with respect to state of the art algorithms the proposed technique enables easy tuning of the required coding redundancy moreover the generated streams are fully compatible with part 1 of the standard

guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems abstract this paper presents incomplete decompositions for various types of matrices as they occur in the implicit discretisation of practical problems a review is given of methods for the usual five point discretisation of a self adjoint elliptic second order partial differential equation in two dimensions on a square the matrices which occur in this type of problem are symmetric m matrices of very regular structure the convergence behaviour of the different decompositions for this case is demonstrated by numerical experiments the paper also gives decompositions for the following type of matrices i symmetric m matrices of a different structure ii symmetric positive definite matrices iii non symmetric matrices

a balanced force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework a new balanced force algorithm is presented for modeling interfacial flow with surface tension the algorithm is characterized by a pressure correction method with the interfaces represented by volume fractions within this flow algorithm we devise a continuous e g continuum surface tension model and a sharp e g a ghost fluid method interface representation of the surface tension induced interfacial pressure jump condition the sharp interface representation is achieved by temporarily reconstructing distance functions from volume fractions we demonstrate that a flow algorithm designed to legislate force balance retains an exact balance between surface tension forces and the resulting pressure gradients this balance holds for both continuous and sharp representations of interfacial surface tension the algorithm design eliminates one of the elusive impediments to more accurate models of surface tension driven flow the remaining of which is accurate curvature estimation to validate our formulation we present results for an equilibrium static drop in two and three dimensions having an arbitrary density jump across the interface we find that the sharp surface tension method yields an abrupt pressure jump across the interface whereas the continuous surface tension method results in a smoother transition both methods however yield spurious velocities of the same order the origin of which is due solely to errors in curvature dynamic results are also presented to illustrate the versatility of the method

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

an adaptive level set method with enhanced volume conservation for simulations in multiphase domains while implicit interface methods such as the level set method have the main advantage of avoiding explicit interface meshing they raise important volume conservation issues that can be handled by local mesh refinement this refinement is then performed multiple times throughout the simulation in order to follow the interface nevertheless mesh adaptation itself is a process that generates a volume conservation problem due to field transfer in this work multiphase simulations are addressed using a new lagrangian level set method that relies on an automatic mesh motion and topological mesh adaptation procedure remeshing is hence activated only when element flipping is detected this procedure is extended in order to take into account local phase distributions during remeshing so that volume conservation can be controlled 2 this method relies on a robust level set reinitialization technique also developed in this work 1 this constraint on volume conservation is automatically relaxed when necessary in order to take into account complex topological events such as apperance disappearance and coalescence of objects during the simulation numerical results show that the proposed method is competitive in terms of cost and accuracy with respect to standard eulerian and lagrangian level set methods while still enabling large displacements and deformations some examples concerning the modeling of evolutive microstructures will be detailed references 1 m shakoor b scholtes p o bouchard and m bernacki an efficient and parallel level set reinitialization method application to micromechanics and microstructural evolutions applied mathematical modelling 39 23 24 7291 7302 2015 2 m shakoor p o bouchard and m bernacki an adaptive level set method with enhanced volume conservation for simulations in multiphase domains international journal for numerical methods in engineering volume 109 issue 4 27 january 2017 555 576

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

tracking discontinuities in hyperbolic conservation laws with spectral accuracy it is well known that the spectral solutions of conservation laws have the attractive distinguishing property of infinite order convergence also called spectral accuracy when they are smooth e g c canuto m y hussaini a quarteroni t a zang spectral methods for fluid dynamics springer verlag heidelberg 1988 j p boyd chebyshev and fourier spectral methods second ed dover new york 2001 c canuto m y hussaini a quarteroni t a zang spectral methods fundamentals in single domains springer verlag berlin heidelberg 2006 if a discontinuity or a shock is present in the solution this advantage is lost there have been attempts to recover exponential convergence in such cases with rather limited success the aim of this paper is to propose a discontinuous spectral element method coupled with a level set procedure which tracks discontinuities in the solution of nonlinear hyperbolic conservation laws with spectral convergence in space spectral convergence is demonstrated in the case of the inviscid burgers equation and the one dimensional euler equations

optimal filter banks for multiple description coding analysis and synthesis multiple description md coding is a source coding technique for information transmission over unreliable networks in md coding the coder generates several different descriptions of the same signal and the decoder can produce a useful reconstruction of the source with any received subset of these descriptions in this paper we study the problem of md coding of stationary gaussian sources with memory first we compute an approximate md rate distortion region for these sources which we prove to be asymptotically tight at high rates this region generalizes the md rate distortion region of el gamal and cover 1982 and ozarow 1980 for memoryless gaussian sources then we develop an algorithm for the design of optimal two channel biorthogonal filter banks for md coding of gaussian sources we show that optimal filters are obtained by allocating the redundancy over frequency with a reverse water filling strategy finally we present experimental results which show the effectiveness of our filter banks in the low complexity low rate regime

numerical schemes for the hamilton jacobi and level set equations on triangulated domains borrowing from techniques developed for conservation law equations numerical schemes which discretize the hamilton jacobi h j level set and eikonal equations on triangulated domains are presented the first scheme is a provably monotone discretization for the h j equations unfortunately the basic scheme lacks lipschitz continuity of the numerical hamiltonian by employing a virtual edge flipping technique local lipschitz continuity of the numerical flux is restored on acute triangulations next schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous hamiltonians these schemes possess a discrete maximum principle on arbitrary triangulations and exhibit local lipschitz continuity of the numerical hamiltonian finally a class of petrov galerkin approximations is considered these schemes are stabilized via a least squares bilinear form the petrov galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy discretization of the level set equation also requires the numerical approximation of a mean curvature term a simple mass lumped galerkin approximation is presented in section 6 and analyzed using maximum principle analysis the use of unstructured meshes permits several forms of mesh adaptation which have been incorporated into numerical examples these numerical examples include discretizations of convex and nonconvex forms of the h j equation the eikonal equation and the level set equation

resolving small scale structures in boussinesq convection by adaptive grid methods inviscid boussinesq convection is a challenging problem both analytically and numerically due to the complex dynamic development of small scales and the rapid loss of solution regularity the boussinesq convection pushes any numerical strategy to the limit in e and shu phys fluids 6 1994 49 a detailed numerical study of the boussinesq convection in the absence of viscous effects is carried out using filtered pseudospectral method and a high order accurate eno schemes in their computations very fine grids have to be used in order to resolve the small structures of the boussinesq fluid in this work we will develop an efficient adaptive grid method for solving the inviscid incompressible flows which can be useful in resolving extremely small structures with reasonably small number of grid points to demonstrate the effectiveness of the proposed method the boussinesq convection problem will be computed using the adaptive grid method

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

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

a stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows a numerical method for the simulation of three dimensional incompressible two phase flows is presented the proposed algorithm combines an implicit pressure stabilized finite element method for the solution of incompressible two phase flow problems with a level set method implemented with a quadrature free discontinuous galerkin dg method e marchandise j f remacle n chevaugeon a quadrature free discontinuous galerkin method for the level set equation journal of computational physics 212 2006 338 357 the use of a fast contouring algorithm n chevaugeon e marchandise c geuzaine j f remacle efficient visualization of high order finite elements international journal for numerical methods in engineering permits us to localize the interface accurately by doing so we can compute the discontinuous integrals without neither introducing an interface thickness nor reinitializing the level set the capability of the resulting algorithm is demonstrated with large scale numerical examples free surface flows dam break sloshing and small scale ones two phase poiseuille rayleigh taylor instability