a gas kinetic scheme for the baer nunziato two phase flow model numerical methods for the baer nunziato bn two phase flow model have attracted much attention in recent years in this paper we present a new gas kinetic scheme for the bn two phase flow model containing non conservative terms in the framework of finite volume method in the view of microscopic aspect a generalized bhatnagar gross krook bgk model which matches with the bn model is constructed based on the integral solution of the generalized bgk model we construct the distribution functions at the cell interface then numerical fluxes can be obtained by taking moments of the distribution functions and non conservative terms are explicitly introduced into the construction of numerical fluxes in this method not only the complex iterative process of exact solutions is avoided but also the non conservative terms included in the equation can be handled well

modeling hyperelasticity in non equilibrium multiphase flows the aim of this article is the construction of a multiphase hyperelastic model the eulerian formulation of the hyperelasticity represents a system of 14 conservative partial differential equations submitted to stationary differential constraints this model is constructed with an elegant approach where the specific energy is given in separable form the system admits 14 eigenvalues with 7 characteristic eigenfields the associated riemann problem is not easy to solve because of the presence of 7 waves the shear waves are very diffusive when dealing with the full system in this paper we use a splitting approach to solve the whole system using 3 sub systems this method reduces the diffusion of the shear waves while allowing to use a classical approximate riemann solver the multiphase model is obtained by adapting the discrete equations method this approach involves an additional equation governing the evolution of a phase function relative to the presence of a phase in a cell the system is integrated over a multiphase volume control finally each phase admits its own equations system composed of three sub systems one and three dimensional test cases are presented

a new level set model for multimaterial flows we propose a new level set model for representing multimaterial flows in multiple space dimensions instead of associating a level set function with a specific fluid material the function is associated with a pair of materials and the interface that separates them a voting algorithm collects sign information from all level set functions and determines material designation to represent a general m material configuration m m 1 2 level set functions need to be accounted for problems of practical interest use far fewer functions as not all pairs of materials share an interface and level set functions that coincide are grouped together under this model regions of potential material ambiguity i e overlaps or vacuum are markedly reduced in size in 2d ambiguous regions are points as opposed to lines in material based level set models in 3d they are lines as opposed to surfaces the model produces excellent results without the need for reinitialization thereby avoiding additional computational costs and preventing excessive numerical diffusion

a discrete action principle for electrodynamics and the construction of explicit symplectic integrators for linear non dispersive media in this work we derive a discrete action principle for electrodynamics that can be used to construct explicit symplectic integrators for maxwell s equations different integrators are constructed depending on the choice of discrete lagrangian used to approximate the action by combining discrete lagrangians in an explicit symplectic partitioned runge kutta method an integrator capable of achieving any order of accuracy is obtained using the von neumann stability analysis we show that the integrators greatly increase the numerical stability and reduce the numerical dispersion compared to other methods for practical purposes we demonstrate how to implement the integrators using many features of the finite difference time domain method however our approach is also applicable to other spatial discretizations such as those used in finite element methods using this implementation numerical examples are presented that demonstrate the ability of the integrators to efficiently reduce and maintain a minimal amount of numerical dispersion particularly when the time step is less than the stability limit the integrators are therefore advantageous for modeling large inhomogeneous computational domains

a musta scheme for a nonconservative two fluid model we present a multistage centered scheme of the kind proposed by toro appl numer math 56 2006 pp 1464 1479 for numerically resolving the simultaneous flow of two fluids through a transport pipeline this model contains nonconservative terms in both the temporal and spatial derivatives and an extension of the standard numerical framework for conservation laws is needed in this paper we rewrite the model in an equivalent mathematical form eliminating the nonconservative time derivatives this allows us to use the framework described by pares siam j numer anal 44 2006 pp 300 321 we develop force and musta type schemes which are consistent with pares formalism numerical simulations demonstrate a high degree of stability of our proposed schemes comparisons with the roe and rusanov schemes indicate that convergence to near identical solutions is obtained when the nonconservative terms are discretized with respect to the same evaluation of the path dependent integrals however if the schemes are not mutually formally path consistent in the sense of pares different converged solutions are obtained

an interface capturing method for the simulation of multi phase compressible flows a novel finite volume interface contact capturing method is presented for simulation of multi component compressible flows with high density ratios and strong shocks in addition the materials on the two sides of interfaces can have significantly different equations of state material boundaries are identified through an interface function which is solved in concert with the governing equations on the same mesh for long simulations the method relies on an interface compression technique that constrains the thickness of the diffused interface to a few grid cells throughout the simulation this is done in the spirit of shock capturing schemes for which numerical dissipation effectively preserves a sharp but mesh representable shock profile for contact capturing the formulation is modified so that interface representations remain sharp like captured shocks countering their tendency to diffuse via the same numerical diffusion needed for shock capturing special techniques for accurate and robust computation of interface normals and derivatives of the interface function are developed the interface compression method is coupled to a shock capturing compressible flow solver in a way that avoids the spurious oscillations that typically develop at material boundaries convergence to weak solutions of the governing equations is proved for the new contact capturing approach comparisons with exact riemann problems for model one dimensional multi material flows show that the interface compression technique is accurate the method employs cartesian product stencils and therefore there is no inherent obstacles in multiple dimensions examples of two and three dimensional flows are also presented including a demonstration with significantly disparate equations of state a shock induced collapse of three dimensional van der waal s bubbles air in a stiffened equation of state liquid water adjacent to a mie gruneisen equation of state wall copper

a relaxation projection method for compressible flows part ii artificial heat exchanges for multiphase shocks the relaxation projection method developed in saurel et al r saurel e franquet e daniel o le metayer a relaxation projection method for compressible flows part i the numerical equation of state for the euler equations j comput phys 2007 822 845 is extended to the non conservative hyperbolic multiphase flow model of kapila et al a k kapila menikoff j b bdzil s f son d s stewart two phase modeling of deflagration to detonation transition in granular materials reduced equations physics of fluids 13 10 2001 3002 3024 this model has the ability to treat multi temperatures mixtures evolving with a single pressure and velocity and is particularly interesting for the computation of interface problems with compressible materials as well as wave propagation in heterogeneous mixtures the non conservative character of this model poses however computational challenges in the presence of shocks the first issue is related to the riemann problem resolution that necessitates shock jump conditions thanks to the rankine hugoniot relations proposed and validated in saurel et al r saurel o le metayer j massoni s gavrilyuk shock jump conditions for multiphase mixtures with stiff mechanical relaxation shock waves 16 3 2007 209 232 exact and approximate 2 shocks riemann solvers are derived however the riemann solver is only a part of a numerical scheme and non conservative variables pose extra difficulties for the projection or cell average of the solution it is shown that conventional godunov schemes are unable to converge to the exact solution for strong multiphase shocks this is due to the incorrect partition of the energies or entropies in the cell averaged mixture to circumvent this difficulty a specific lagrangian scheme is developed the correct partition of the energies is achieved by using an artificial heat exchange in the shock layer with the help of an asymptotic analysis this heat exchange takes a similar form as the pseudoviscosity introduced by von neumann and richtmyer j von neumann r d richtmyer a method for the numerical calculation of hydrodynamic shocks j appl phys 21 1950 232 237 the present lagrangian numerical scheme thus combines riemann solvers and artificial heat exchanges an eulerian variant is then obtained by using the relaxation projection method developed earlier by the authors for the euler equations the method is validated against exact solutions based on the multiphase shock relations as well as exact solutions of the euler equations in the context of interface problems the method is able to solve interfaces separating pure fluids or heterogeneous mixtures with very large density ratio and with very strong shocks

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

stochastic discrete equation method sdem for two phase flows a new scheme for the numerical approximation of a five equation model taking into account uncertainty quantification uq is presented in particular the discrete equation method dem for the discretization of the five equation model is modified for including a formulation based on the adaptive semi intrusive asi scheme thus yielding a new intrusive scheme sdem for simulating stochastic two phase flows some reference test cases are performed in order to demonstrate the convergence properties and the efficiency of the overall scheme the propagation of initial conditions uncertainties is evaluated in terms of mean and variance of several thermodynamic properties of the two phases

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

simulation of compressible two phase flows with topology change of fluid fluid interface by a robust cut cell method we develop a robust cut cell method for numerical simulation of compressible two phase flows with topology change of the fluid fluid interface in cut cell methods the flows can be solved in the finite volume framework and the jump conditions at the interface are resolved by solving a local riemann problem therefore cut cell methods can obtain interface evolution with high resolution and at the same time satisfactorily maintain the conservation of flow quantities however it remains a challenge for the cut cell methods to handle interfaces with topology change or very high curvature where the mesh is not sufficiently fine to resolve the interface inappropriate treatment could give rise to either distorted interface advection or unphysical oscillation of flow variables especially when the regularization process e g reinitialization in the level set methods is implemented a robust cut cell method is proposed here with the interface being tracked by a level set function the local unphysical oscillation of flow variables in the presence of topology change is shown to be greatly suppressed by using a delayed reinitialization the method can achieve second order accuracy with respect to the interface position in the absence of topology changes of interface while locally degrading to first order at the interface region where topology change occurs its performance is examined through a variety of numerical tests such as rayleigh collapse shock bubble interaction and shock induced bubble collapse in water numerical results are compared against either benchmark solutions or experimental observations and good agreement has been achieved qualitatively and or quantitatively finally we apply the method to investigating the collapse process of two tandem bubbles in water

interaural correlation sensitivity sensitivity to differences in interaural correlation was measured for 1 3 erb wide bands of noise using a 2ifc task at six frequencies 250 500 750 1000 1250 and 1500 hz the sensitivity index d was measured for discriminations between a number of fixed pairs of correlation values cumulative d functions were derived for each frequency and condition the d for discriminating any two values of correlation may be recovered from the cumulative d function by the difference between cumulative d s for these values two conditions were employed the noisebands were either presented in isolation narrow band condition or in the context of broad contiguous flanking bands of correlated noise fringed condition the cumulative d functions showed greater sensitivity to differences in correlation close to 1 than close to 0 at low frequencies but this difference was less pronounced in the fringed condition also a more linear relationship was observed when cumulative d was plotted as a function of the equivalent signal to noise ratio snr in db for each correlation value rather than directly against correlation the equivalent snr was the snr at which the interaural correlation in an nos stimulus would equal the interaural correlation of the noise used in the experiment the maximum cumulative d declined above 750 hz this decline was steeper for the fringed than for the narrow band condition for the narrow band condition the total cumulative d was variable across listeners all cumulative d functions were closely fitted using a simple two parameter function the complete data sets averaged across listeners from the fringed and narrow band conditions were fitted using functions to describe the changes in these parameters over frequency in order to produce an interpolated family of curves that describe sensitivity at frequencies between those tested these curves predict the spectra recovered by the binaural system when complex sounds such as speech are masked by noise

detection of static and dynamic changes in interaural correlation this study examines the relation between a static and a dynamic measure of interaural correlation discrimination 1 the just noticeable difference jnd in interaural correlation and 2 the minimum detectable duration of a fixed interaural correlation change embedded within a single noise burst of a given reference correlation for the first task jnds were obtained from reference interaural correlations of 1 1 and from 0 interaural correlation in either the positive or negative direction for the dynamic task duration thresholds were obtained for a brief target noise of 1 1 and 0 interaural correlation embedded in reference marker noise of 1 1 and 0 interaural correlation performance with a reference interaural correlation of 1 was significantly better than with a reference correlation of 1 similarly when the reference noise was interaurally uncorrelated discrimination was significantly better for a target correlation change towards 1 than towards 1 thus for both static and dynamic tasks interaural correlation discrimination in the positive range was significantly better than in the negative range using the two measures the length of a binaural temporal window was estimated its equivalent rectangular duration erd was approximately 86 ms and independent of the interaural correlation configuration

mathematical and numerical modeling of two phase compressible flows with micro inertia a new model with full coupling between micro and macroscale motion is developed for compressible multiphase mixtures the equations of motion and the coupling microstructural equation an analogue of the rayleigh lamb equation are obtained by using the hamilton principle of stationary action in the particular case of bubbly fluids the resulting model contains eight partial differential equations one dimensional case and is unconditionally hyperbolic the equations are solved numerically by an adapted godunov method the model and methods are validated for two very different test problems the first one consists of a wave propagating in a liquid containing a small quantity of gas bubbles computed oscillating shock waves fit perfectly the experimental data then the one dimensional multiphase model is used as a reduction tool for the multidimensional interaction of a shock wave with a large bubble good agreement is again obtained

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

discrete equations for physical and numerical compressible multiphase mixtures we have recently proposed in 21 a compressible two phase unconditionally hyperbolic model able to deal with a wide range of applications interfaces between compressible materials shock waves in condensed multiphase mixtures homogeneous two phase flows bubbly and droplet flows and cavitation in liquids one of the difficulties of the model as always in this type of physical problems was the occurrence of non conservative products in 21 we have proposed a discretisation technique that was without any ambiguity only in the case of material interfaces not in the case of shock waves this model was extended to several space dimensions in 24 in this paper thanks to a deeper analysis of the model we propose a class of schemes that are able to converge to the correct solution even when shock waves interact with volume fraction discontinuities this analysis provides a more accurate estimate of closure terms but also an accurate resolution method for the conservative fluxes as well as non conservative terms even for situations involving discontinuous solutions the accuracy of the model and method is clearly demonstrated on a sequence of difficult test problems

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

adaptive osher type scheme for the euler equations with highly nonlinear equations of state abstract for the numerical simulation of detonation of condensed phase explosives a complex equation of state eos such as the jones wilkins lee jwl eos or the cochran chan c c eos are widely used however when a conservative scheme is used for solving the euler equations with such equations of state a spurious solution across the contact discontinuity a well known phenomenon in multi fluid systems arises even for single materials in this work we develop a generalised osher type scheme in an adaptive primitive conservative framework to overcome the aforementioned difficulties resulting numerical solutions are compared with the exact solutions and with the numerical solutions from the godunov method in conjunction with the exact riemann solver for the euler equations with mie gruneisen form of equations of state such as the jwl and the c c equations of state the adaptive scheme is extended to second order and its empirical convergence rates are presented verifying second order accuracy for smooth solutions through a suite of several tests problems in one and two space dimensions we illustrate the failure of conservative schemes and the capability of the methods of this paper to overcome the difficulties

numerical resolution for a compressible two phase flow model based on the theory of thermodynamically compatible systems this paper is concerned with the numerical solution of the equations governing two phase gas solid mixture in the framework of thermodynamically compatible systems theory the equations constitute a non homogeneous system of nonlinear hyperbolic conservation laws a total variation diminishing tvd slope limiter centre slic numerical scheme based on the splitting approach is presented and applied for the solution of the initial boundary value problem for the equations the model equations and the numerical methods are systematically assessed through a series of numerical test cases strong numerical evidence shows that the model and the methods are accurate robust and conservative the model correctly describes the formations of shocks and rarefactions in two phase gas solid flow

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

numerical simulation for two phase flows using hybrid scheme the present paper is devoted to the computation of two phase flows using two fluid approach two difficulties arise for the model one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations to deal with the aforementioned difficulties the non conservative volume fraction equation is discretized by weno scheme and the cweno type central upwind scheme is applied to solve the mass momentum and energy equations computational results are eventually provided and discussed

how to preserve the mass fractions positivity when computing compressible multi component flows abstract we are interested in the numerical investigation of the compressible flow of a gaseous mixture considering a hyperbolic system including the euler equations for the mixture and a mass conservation equation for each species we propose a new approximation scheme for the convective term of the species equations this approximation relies on some properties of the exact solution of the riemann problem for the multi component system and applies when an upwind godunov type scheme is used for the euler equations its main interest lies in the fact that it preserves the positivity and monotonicity of the mass fractions of all species

preventing numerical errors generated by interface capturing schemes in compressible multi material flows in the present work errors generated in computations of compressible multi material flows using shock capturing schemes are examined specifically pressure oscillations when the specific heats ratio is variable but also temperature spikes and species conservation errors these numerical errors are generated at material discontinuities due to an inconsistent treatment of the convective terms though temperature errors are irrelevant to solutions to the euler equations it is shown that they have the potential to lead to problems when physical diffusion is included i e for the navier stokes equations these errors are studied analytically and numerically by considering the one dimensional advection of isolated material discontinuities a methodology preventing such errors for weighted essentially non oscillatory weno schemes is presented in which modified weno weights are used to solve the transport equation for mass fraction in conservative form to prevent temperature and species conservation errors pressure errors are prevented by solving an additional transport equation for a given function of the ratio of specific heats several multi dimensional problems with various discontinuities shocks material interfaces and contact discontinuities including the single mode richtmyer meshkov instability and turbulence are considered to test the method

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

a five equation reduced model for compressible two phase flow problems this paper studies an eulerian diffuse interface model for the simulation of compressible multifluid and two phase flow problems we first show how to derive this model from a seven equation two pressure two velocity model of baer nunziato type using an asymptotic analysis in the limit of zero relaxation time we then study the mathematical properties of the system the structure of the waves the expression of the riemann s invariants and the existence of a mathematical entropy we also describe two different numerical approximation schemes for this system the first one relies on a linearized riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations finally we present some numerical experiments and comparisons with the results obtained by the two pressure two velocity model as well as some test cases and comparisons with another five equation model recently proposed for interface computations between compressible fluids

viscous shock profiles and primitive formulations weak solutions of hyperbolic systems in primitive nonconservative form for which a consistent conservation form exists are considered it is shown that for primitive formulations shock relations are not uniquely defined by the states to either side of the shock but also depend on the viscous path connecting the two consistent viscous shock profiles are enforced by adding scheme dependent small viscous perturbations that account for leading order conservation errors the resulting primitive algorithm is conservative to the order of the approximation one dimensional euler calculations of flows containing weak to moderate shocks show that conservation errors in primitive calculations are substantially reduced by including the viscous perturbation terms while not eliminating conservation errors entirely it is found that for a wide range of problems both conservative and primitive flow calculations are of comparable quality

a robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state this paper addresses issues in high fidelity numerical simulations of transcritical turbulent flows at supercritical pressure the proposed strategy builds on a tabulated look up table method based on refprop database for an accurate estimation of non linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions based on the look up table method we propose a numerical method that satisfies high order spatial accuracy spurious oscillation free property and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface the method introduces artificial mass diffusivity to the continuity and momentum equations in a physically consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious oscillation free property in the velocity field the pressure evolution equation is derived from the full compressible navier stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look up table method flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness accuracy and consistency of the proposed approach

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 simple interface sharpening technique with a hyperbolic tangent function applied to compressible two fluid modeling a simple interface sharpening technique based on hyperbolic tangent interpolation which was proposed in the previous study f xiao y honma k kono a simple algebraic interface capturing scheme using hyperbolic tangent function int j numer methods fluids 48 2005 1023 1040 is applied to the compressible two fluid modeling the implementation of this scheme is very simple the interpolation of the volume fraction in the monotonicity upwind scheme for conservation law muscl solver is just replaced by the hyperbolic tangent interpolation while the muscl interpolations for other variables are maintained this technique is limited for the region near the interface to prevent the spurious oscillations of a minor phase the one dimensional and two dimensional problems are solved and the results are compared with those of the original muscl solver the results show that the interface is significantly sharpened with this technique and its sharpness is well controlled by one parameter in addition the robustness of the scheme does not change with sharpening the interface in the range we investigated an interface sharpening technique is proposed for compressible two fluid modeling this method simply uses the hyperbolic tangent interpolation for volume fraction interface thickness is well controlled by one parameter in the scheme

multicomponent gas flow computations by a discontinuous galerkin scheme using l2 projection of perfect gas eos a new formulation of multicomponent gas flow computation suited to a discontinuous galerkin discretization is here presented and discussed the original key feature is the use of l 2 projection form of the perfect gas equation of state that allows all thermodynamic variables to span the same functional space this choice greatly mitigates problems encountered by the front capturing schemes in computing discontinuous flow field retaining at the same time their conservation properties at the discrete level and ease of use this new approach combined with an original residual based artificial dissipation technique shows itself capable through a series of tests illustrated in the paper to both control the spurious oscillations of flow variables occurring in high order accurate computations and reduce them increasing the degree of the polynomial representation of the solution this result is of great importance in computing reacting gaseous flows where the local accuracy of temperature and species mass fractions is crucial to the correct evaluation of the chemical source terms contained in the equations even if the presence of the physical diffusivities somewhat brings relief to these problems the present work can therefore also be considered among many others already presented in the literature as the authors first step toward the construction of a new discontinuous galerkin scheme for reacting gas mixture flows

numeric treatment of contact discontinuity with multi gases in this paper we work with a finite volume procedure for the computation of the one dimensional euler equations for the treatment of multi gases and the problem of the correct treatment of the discontinuity was more nearly investigated a suggested equation was embedded in the finite volumes context and implemented in our code accordingly and regarded as validated

a compressible navier stokes flow solver with scalar transport this paper concerns the extension of the gas kinetic scheme for the compressible navier stokes equations to the flow calculation with interfaces and mixing the objective of the current research targets mainly on the accurate capturing of navier stokes diffusive interfaces where the thickness can be resolved by the cell size firstly a new bgk ns scheme coupling with the level set type scalar function transport is constructed even though the scalar function is directly incorporated into the gas distribution function and it evolves according to the gas kinetic equation it likes more or less a color function which has no direct contribution for the time evolution of conservative flow variables such as mass momentum and energy due to the coupling of the scalar function into the gas kinetic formulation the governing equations for the scalar function turns out to be an advection diffusion equations and the diffusive coefficient can be controlled by the particle collision time which makes the current scheme suitable for the gas mixing problems with a controllable diffusion coefficients however for the non mixing or sharp interface problems such as the interface between gas and liquid the current method can be used as a scheme similar to the level set method where the interface location can be identified with a fixed level set value such as q 0 the current method is applied to a few examples from the simple square wave propagation and diffusion to the 3d rayleigh taylor instability the supersonic mixing layer and the shock helium bubble interaction case show clearly the convergence of the current navier stokes solver for the flow problems with mixing of components and interface once the interface thickness can be well resolved by the cell size in the case of shock hitting sf6 cylinder the computation predicts the experimental measure very well in the current scheme the schmidt number can be freely chosen according to the physical reality

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

liquid and liquid gas flows at all speeds all speed flows and in particular low mach number flow algorithms are addressed for the numerical approximation of the kapila et al 1 multiphase flow model this model is valid for fluid mixtures evolving in mechanical equilibrium but out of temperature equilibrium and is efficient for material interfaces computation separating miscible and non miscible fluids in this context the interface is considered as a numerically diffused zone captured as well as all present waves shocks expansion waves the same flow model can be used to solve cavitating and boiling flows 2 many applications occurring with liquid gas interfaces and cavitating flows involve a very wide range of mach number from 10 3 to supersonic and even hypersonic conditions with respect to the mixture sound speed it is thus important to address numerical methods free of restrictions regarding the mach number to do this a preconditioned riemann solver is built and embedded into the godunov explicit scheme it is shown that this method converges to exact solutions but needs too small time steps to be efficient an implicit version is then derived first in one dimension and second in the frame of 2d unstructured meshes two phase flow preconditioning is then addressed in the frame of the saurel et al 3 algorithm modifications of the preconditioned riemann solver are needed and detailed convergence of both single phase and two phase numerical solutions are demonstrated with the help of single phase and two phase steady nozzle flow solutions last the method is illustrated by the computation of real cavitating flows in venturi nozzles vapour pocket size and instability frequencies are reproduced by the model and method without using any adjustable parameter

multi solid and multi fluid diffuse interface model we extend the model of diffuse solid fluid interfaces developed earlier by authors of this paper to the case of arbitrary number of interacting hyperelastic solids plastic transformations of solids are taken into account through a maxwell type model the specific energy of each solid is given in separable form it is the sum of a hydrodynamic part of the energy depending only on the density and the entropy and an elastic part of the energy which is unaffected by the volume change it allows us to naturally pass to the fluid description in the limit of vanishing shear modulus in spite of a large number of governing equations the model has a quite simple mathematical structure it is a duplication of a single visco elastic model the model is well posed both mathematically and thermodynamically it is hyperbolic and compatible with the second law of thermodynamics the resulting model can be applied in the situations involving an arbitrary number of fluids and solids in particular we show the ability of the model to describe spallation and penetration phenomena occurring during high velocity impacts

an algorithm for les of premixed compressible flows using the conditional moment closure model a novel numerical method has been developed to couple a recent high order accurate fully compressible upwind method with the conditional moment closure combustion model the governing equations turbulence modelling and numerical methods are presented in full the new numerical method is validated against direct numerical simulation dns data for a lean premixed methane slot burner although the modelling approaches are based on non premixed flames and hence not expected to be valid for a wide range of premixed flames the predicted flame is just 10 longer than that in the dns and excellent agreement of mean mass fractions conditional mass fractions and temperature is demonstrated this new numerical method provides a very useful framework for future application of cmc to premixed as well as non premixed combustion

the modified ghost fluid method for coupling of fluid and structure constituted with hydro elasto plastic equation of state in this work the modified ghost fluid method mgfm t g liu b c khoo and k s yeo j comput phys 190 2003 pp 651 681 is further developed and applied to treat the compressible fluid compressible structure coupling to facilitate theoretical analysis the structure is modeled as elastic plastic material with perfect plasticity and constituted with the hydro elasto plastic equation of state h s tang and f sotiropoulos j comput phys 151 1999 pp 790 815 under strong impact this results in the coupled compressible fluid compressible structure system which is fully hyperbolic to understand the effect of structure deformation on the interfacial and flow status the compressible fluid compressible structure riemann problem is analyzed in the consideration of material deformation with an approximate riemann problem solver proposed to take into account the effect of material elastic plastic deformation we clearly show the ghost fluid method can be applied to treat the flow deformable structure coupling under strong impact provided that a proper riemann problem solver is used to predict the ghost fluid states and the resultant mgfm can work effectively and efficiently in such situations various examples are presented to validate and support the conclusions reached

auditory evoked potentials to changes in interaural cross correlation the objective of this study is to analyze the representation of specific binaural stimulus features in the human brain and to compare the results to psychoacoustic data late auditory evoked potentials to changes in the interaural cross correlation iacc of continuous bandpass noise 100 2000 hz were recorded 1000 sweeps per stimulus condition were averaged in experiment 1 a brief binaural gap with a gap iacc was interposed in the noise with a reference iacc n1 and p2 amplitudes increased with increasing gap duration for uncorrelated reference iacc 0 1 0 and 0 1 0 conditions objective thresholds were comparable to psychoacoustic data for uncorrelated gap iacc 1 0 1 and 1 0 1 conditions objective thresholds were about four times larger than in psychoacoustic measurements in experiment 2 reference and test interval had the same length of 800 ms and the magnitude of change in iacc was varied objective iacc jnds are larger for an uncorrelated reference than for iaccs of 1 for the uncorre

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

diffuse interface model for compressible fluid compressible elastic plastic solid interaction an eulerian hyperbolic diffuse interface model for elastic plastic solid fluid interaction is constructed the system of governing equations couples euler equations of compressible fluids and a visco plastic model of maxwell type materials the deviatoric part of the stress tensor decreases during plastic deformations in the same manner as models of multicomponent fluids in particular the model is able to create interfaces which were not present initially the model is thermodynamically compatible it verifies the entropy inequality however a numerical treatment of the model is particularly challenging indeed the model is non conservative so a special numerical splitting is proposed to overcome this difficulty the numerical algorithm contains two relaxation procedures one of them is physical and is related to the plastic relaxation mechanism relaxation toward the yield surface the second one is numerical it consists in replacing the algebraic equation expressing a mechanical equilibrium between components by a partial differential equation with a short relaxation time the numerical method was tested in 1d case wilkins flying plate problem 2d plane case impact of a projectile on a plate and axisymmetrical case taylor test problem impact with penetration effects etc numerical examples show the ability of the model to deal with real physical phenomena

a runge kutta discontinuous galerkin approach to solve reactive flows a runge kutta discontinuous galerkin method to solve the hyperbolic part of reactive navier stokes equations written in conservation form is presented complex thermodynamics laws are taken into account particular care has been taken to solve the stiff gaseous interfaces correctly with no restrictive hypothesis 1d and 2d test cases are presented

solid fluid diffuse interface model in cases of extreme deformations diffuse interface methods have been recently proposed and successfully used for accurate compressible multi fluid computations abgrall 1 kapila et al 20 saurel et al 30 these methods deal with extended systems of hyperbolic equations involving a non conservative volume fraction equation and relaxation terms following the same theoretical frame we derive here an eulerian diffuse interface model for elastic solid compressible fluid interactions in situations involving extreme deformations elastic effects are included following the eulerian conservative formulation proposed in godunov 16 miller and colella 23 godunov and romenskii 17 plohr and plohr 27 and gavrilyuk et al 14 we apply first the hamilton principle of stationary action to derive the conservative part of the model the relaxation terms are then added which are compatible with the entropy inequality in the limit of vanishing volume fractions the euler equations of compressible fluids and a conservative hyperelastic model are recovered it is solved by a unique hyperbolic solver valid at each mesh point pure fluid pure solid and mixture cell capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid

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 five equation model for the simulation of miscible and viscous compressible fluids abstract typical multispecies compressible navier stokes computations employ conservative equations for mass fraction transport upwind discretisations of these governing equations produce spurious pressure oscillations at diffuse contact surfaces between gases of differing ratio of specific heat capacities which degrade the convergence rate of the algorithm adding quasi conservative equations for volume fraction can solve this error however this approach has been derived only for immiscible fluids here a five equation quasi conservative model is proposed that includes the effects of species diffusion viscosity and thermal conductivity the derivation of the model is presented along with a numerical method to solve the governing equations at second order accuracy in space and time formal convergence studies demonstrate the expected order of accuracy is achieved for three benchmark problems cross validated against two standard mass fraction models in these test cases the new model has between 2 and 10 times lower error for a given grid size simulations of a two dimensional air sf6 richtmyer meshkov instability demonstrate that the new model converges to the solution with four times fewer points in each direction when compared to the mass fraction model in an identical numerical framework this represents an 40 times lower computational cost for an equivalent error in two dimensional computations the proposed model is thus very suitable for direct numerical simulation and large eddy simulation of compressible mixing

weakly implicit numerical schemes for a two fluid model the aim of this paper is to construct semi implicit numerical schemes for a two phase two fluid flow model allowing for violation of the cfl criterion for sonic waves while maintaining a high level of accuracy and stability on volume fraction waves by using an appropriate hybridization of a robust implicit flux and an upwind explicit flux we obtain a class of first order schemes which we refer to as weakly implicit mixture flux wimf methods in particular by using an advection upstream splitting method ausmd type of upwind flux s evje and t flatten j comput phys 192 2003 pp 175 210 we obtain a scheme denoted as wimf ausmd we present several numerical simulations all of them indicating that the cfl stability of the wimf ausmd scheme is governed by the velocity of the volume fraction waves and not the rapid sonic waves comparisons with an explicit roe scheme indicate that the scheme presented in this paper is highly efficient robust and accurate on slow transients by exploiting the possibility to take much larger time steps it outperforms the roe scheme in the resolution of the volume fraction wave for the classical water faucet problem on the other hand it is more diffusive on pressure waves although conservation of positivity for the masses is not proved we demonstrate that a fix may be applied making the scheme able to handle the transition to one phase flow while maintaining a high level of accuracy on volume fraction fronts

riemann problem and level set approaches for homentropic two fluid flow computations a finite volume method is presented for the computation of compressible flows of two immiscible fluids at very different densities a novel ingredient in the method is a linearized two fluid osher scheme allowing for flux computations in the case of different fluids e g water and air left and right of a cell face a level set technique is employed to distinguish between the two fluids the level set equation is incorporated into the system of hyperbolic conservation laws fixes are presented for the solution errors pressure oscillations that may occur near two fluid interfaces when applying a capturing method the fixes are analyzed and tested for two fluid flows with arbitrarily large density ratios a simple variant of the ghost fluid method appears to be a perfect remedy computations for compressible water air flows yield perfectly sharp pressure oscillation free interfaces the masses of the separate fluids appear to be conserved up to first order accuracy

accurate computation of contact discontinuities in flows with general equations of state abstract the evolution of a contact discontinuity in a real fluid flow is particularly difficult to compute with a conservative scheme indeed godunov type schemes involve an averaging step which may create an intermediate state with an incorrect pressure spurious acoustic waves are then generated these waves affect transient simulations as well as implicit time marching procedures for steady state computations however a formulation involving the pressure as a dependent variable can be used to restore a fast convergence for steady state computations

direct numerical simulation of interfacial instabilities a consistent conservative all speed sharp interface method we present a conservative and consistent numerical method for solving the navier stokes equations in flow domains that may be separated by any number of material interfaces at arbitrarily high density viscosity ratios and acoustic impedance mismatches subjected to strong shock waves and flow speeds that can range from highly supersonic to near zero mach numbers a principal aim is prediction of interfacial instabilities under superposition of multiple potentially active modes rayleigh taylor kelvin helmholtz richtmyer meshkov as found for example with shock driven immersed fluid bodies locally oblique shocks accordingly we emphasize fidelity supported by physics based validation including experiments consistency is achieved by satisfying the jump discontinuities at the interface within a conservative 2nd order scheme that is coupled in a conservative manner to the bulk fluid motions the jump conditions are embedded into a riemann problem solved exactly to provide the pressures and velocities along the interface which is tracked by a level set function to accuracy of o dx 5 dt 4 subgrid representation of the interface is achieved by allowing curvature of its constituent interfacial elements to obtain o dx 3 accuracy in cut cell volume with attendant benefits in calculating cell geometric features and interface curvature o dx 3 overall the computation converges at near theoretical o dx 2 spurious currents are down to machine error and there is no time step restriction due to surface tension our method is built upon a quadtree like adaptive mesh refinement infrastructure when necessary this is supplemented by body fitted grids to enhance resolution of the gas dynamics including flow separation shear layers slip lines and critical layers comprehensive comparisons with exact solutions for the linearized rayleigh taylor and kelvin helmholtz problems demonstrate excellent performance sample simulations of liquid drops subjected to shock waves demonstrate for the first time ab initio numerical prediction of the key interfacial features and phenomena found in recent experimental and theoretical studies of this class of problems t g theofanous aerobreakup of newtonian and viscoelastic liquids ann rev fluid mech 43 2011 661 690

an exact riemann solver for compressible two phase flow models containing non conservative products in this article we present a new numerical procedure for solving exactly the riemann problem of compressible two phase flow models containing non conservative products these products appear in the expressions for the interactions between the two phases thus in the compressible limit the governing equations are hyperbolic but can not be written as conservation laws i e in divergence form in general the solution to the riemann problem of these models contains six distinct centered waves according to the relative position of these waves in the x t plane the possible solutions can be classified into four principal configurations the riemann solver we propose herein investigates sequentially each of these configurations until an admissible solution is calculated special configurations corresponding to coalescence of waves are also analyzed and included in the solver further we examine the accuracy and robustness of three known methods for the integration of the non conservative products via a series of numerical tests finally the issue of existence and uniqueness of solutions to the riemann problem is discussed

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

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