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Numerical Modeling Of TwoPhase Flows Using The TwoFluid TwoPressure Approach
"... this paper, di#usion terms are omitted. Convective terms and source terms (relaxation terms) are taken into account by a fractional step approach. It is well known the latter is not optimal in terms of accuracy (see Ref ..."
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Cited by 19 (8 self)
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this paper, di#usion terms are omitted. Convective terms and source terms (relaxation terms) are taken into account by a fractional step approach. It is well known the latter is not optimal in terms of accuracy (see Ref
TransportEquilibrium Schemes for Computing Nonclassical Shocks
 I. Scalar Conservation Laws, preprint, Laboratoire JacquesLouis Lions
, 2005
"... This paper presents a very efficient numerical strategy for computing the weak solutions of scalar conservation laws which fail to be genuinely nonlinear. We concentrate on the typical situation of either concaveconvex or convexconcave flux functions. In such a situation, nonclassical shocks viola ..."
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Cited by 18 (7 self)
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This paper presents a very efficient numerical strategy for computing the weak solutions of scalar conservation laws which fail to be genuinely nonlinear. We concentrate on the typical situation of either concaveconvex or convexconcave flux functions. In such a situation, nonclassical shocks violating the classical Oleinik entropy criterion must be taken into account since they naturally arise as limits of certain diffusivedispersive regularizations to hyperbolic conservation laws. Such discontinuities play an important part in the resolution of the Riemann problem and their dynamics turns out to be driven by a prescribed kinetic function which acts as a selection principle. It aims at imposing the entropy dissipation rate across nonclassical discontinuities, or equivalently their speed of propagation. From a numerical point of view, the serious difficulty consists in enforcing the kinetic criterion, that is in controling the numerical entropy dissipation of the nonclassical shocks for any given discretization. This is known to be a very challenging issue. By means of an algorithm made of two steps, namely an Equilibrium step and a Transport step, we show how to force the validity of the kinetic criterion at the discrete level. The resulting scheme provides in addition sharp profiles. Numerical evidences illustrate the validity of our approach. 1
A General Technique for Eliminating Spurious Oscillations in Conservative Schemes for Multiphase and Multispecies Euler Equations
 in Conservative Schemes for Multiphase and Multispecies Euler Equations, UCLA CAM Report
, 2000
"... Standard conservative schemes have been shown to admit nonphysical oscillations near some material interfaces. For example, the calorically perfect Euler equations have been shown to admit these oscillations when there is a jump in both temperature and gamma across an interface, but not when either ..."
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Cited by 17 (11 self)
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Standard conservative schemes have been shown to admit nonphysical oscillations near some material interfaces. For example, the calorically perfect Euler equations have been shown to admit these oscillations when there is a jump in both temperature and gamma across an interface, but not when either temperature or gamma is constant [4]. For most problems, one can obtain adequate numerical results by applying a fully conservative method to the mass fraction formulation of the problem. Comparable results can also be obtained with the level UCLA, Research supported in part by ONR N000149710027, ARPA URIONRN00014 92J1890, NSF #DMS 9404942, and ARO DAAH049510155 y UCSB, Research supported in part by NSF DMS9805546 z UCLA, Research supported in part by ONR N000149710027, ARPA URIONRN00014 92J1890, NSF #DMS 9404942, and ARO DAAH049510155 1 set formulation of the problem, as long as gamma is reconstructed in a smooth way from the level set function. Occasionally, the conservative method will admit nonphysical oscillations which can be avoided by application of a nonconservative correction to the total energy on a set of measure zero under grid refinement. We outline this correction method, drawing heavily on the work in [5]. 2 1
Practical computation of axisymmetrical multifluid flows
 International Journal of Finite Volumes
"... Abstract. We adapt the SaurelAbgrall front capturing finite volumes method for an industrial simulation of compressible multifluid flows. We then apply the method to the case of airwater flow in the cooling chamber of an axisymmetrical gas generator. We describe successively how to deal with exac ..."
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Cited by 15 (5 self)
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Abstract. We adapt the SaurelAbgrall front capturing finite volumes method for an industrial simulation of compressible multifluid flows. We then apply the method to the case of airwater flow in the cooling chamber of an axisymmetrical gas generator. We describe successively how to deal with exact and global Riemann solvers, pressure oscillations, unstructured meshes, axisymmetry, boundary conditions and overly restrictive CFL conditions. The resulting algorithm is efficient and robust. 1.
Adaptive characteristicsbased matching for compressible multifluid dynamics
 J. COMPUT. PHYS
, 2005
"... This paper presents an evolutionary step in sharp capturing of shocked, high Acoustic Impedance Mismatch (AIM) interfaces in an adaptive mesh refinement (AMR) environment. The central theme which guides the present development addresses the need to optimize between the algorithmic complexities in a ..."
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Cited by 14 (4 self)
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This paper presents an evolutionary step in sharp capturing of shocked, high Acoustic Impedance Mismatch (AIM) interfaces in an adaptive mesh refinement (AMR) environment. The central theme which guides the present development addresses the need to optimize between the algorithmic complexities in advanced front capturing and front tracking methods developed recently for high AIM interfaces with the simplicity requirements imposed by the AMR multilevel dynamic solutions implementation. The paper shows that we have achieved this objective by means of relaxing the strict conservative treatment of AMR prolongation/restriction operators in the interfacial region and by using a NaturalNeighborInterpolation (NNI) algorithm to eliminate the need for ghost cell extrapolation into the other fluid in a characteristicsbased matching (CBM) scheme. The later is based on a twofluid Riemann solver, which brings the accuracy and robustness of fronttracking approach into the fast local level set frontcapturing implementation of the CBM method. A broad set of test prob
A highresolution Godunov method for compressible multimaterial flow on overlapping grids
 J. Comput. Phys
"... A numerical method is described for inviscid, compressible, multimaterial flow in two space dimensions. The flow is governed by the multimaterial Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and blockstructured adap ..."
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Cited by 14 (8 self)
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A numerical method is described for inviscid, compressible, multimaterial flow in two space dimensions. The flow is governed by the multimaterial Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and blockstructured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a highresolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shockcapturing schemes. The energy correction is constructed based on a uniform pressurevelocity flow and is significant only near the captured interface. A variety of twomaterial flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on the JonesWilkinsLee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady onedimensional shockinterface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gasfilled cylindrical inhomogeneities, and the impulsive motion of the twocomponent mixture in a rigid cylindrical vessel.
Some Recent Finite Volume schemes to Compute Euler Equations Using Real Gas EOS
, 2000
"... This paper deals with the resolution by Finite Volume methods of Eu ]er equations in one space dimension, with real gas state laws (namely perfect gas EOS, Tammann EOS and Van Der Waals EOS). All tests are of shock tube type, in order to examine a wide class of solutions, involving Sod shock tu ..."
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Cited by 14 (5 self)
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This paper deals with the resolution by Finite Volume methods of Eu ]er equations in one space dimension, with real gas state laws (namely perfect gas EOS, Tammann EOS and Van Der Waals EOS). All tests are of shock tube type, in order to examine a wide class of solutions, involving Sod shock tube, stationary shock wave, unsteady contact discontinuity, occurence of vacuum by double rarefaction wave, propagation of a 1rarefaction wave over "vacuum", ... Most of methods computed herein are approximate Godunov solvers: VFRoe, VFFC, VFRoe ncv (r,u,p) and PVRS. The energy relaxation method with VFRoe ncv (r, u,p) and Rusanov scheme have been investigated too. Qualitative results are presented or commented for all test cases and numerical rates of convergence on some test cases have been measured for first and second order (RungeKutta 2 with MUSCL reconstruction) approximations.
Riemannproblem and levelset approaches for twofluid flow computations
 J. Comp. Phys
, 2002
"... A finitevolume 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, twofluid Osher scheme, allowing for flux computations in the case of different fluids (e.g., water and air) left and ..."
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Cited by 13 (2 self)
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A finitevolume 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, twofluid 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 levelset technique is employed to distinguish between the two fluids. The levelset equation is incorporated into the system of hyperbolic conservation laws. Fixes are presented for the solution errors (pressure oscillations) that may occur near twofluid interfaces when applying a capturing method. The fixes are analyzed and tested. For twofluid flows with arbitrarily large density ratios, a simple variant of the ghostfluid method appears to be a perfect remedy. Computations for compressible water–air flows yield perfectly sharp, pressureoscillationfree interfaces. The masses of the separate fluids appear to be conserved up to firstorder accuracy.