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A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). (English) Zbl 0957.76052
From the summary: We propose a new numerical method for treating interfaces in Eulerian schemes that maintains the Heaviside profile of density with no numerical smearing. We use a level set function to track the motion of a multimaterial interface in Eulerian framework. In addition, the use of ghost cells (actually ghost nodes in our finite difference framework) and a new isobaric fix technique allows us to keep the density profile from smearing out, while still keeping the scheme robust and easy to program with simple extensions to multidimensions and multilevel time integration, e.g. by Runge-Kutta methods.

MSC:
76M20Finite difference methods (fluid mechanics)
76N15Gas dynamics, general
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References:
[1] Adalsteinsson, D.; Sethian, J. A.: The fast construction of extension velocities in level set methods. J. comput. Phys. 148, 2 (1998) · Zbl 0919.65074
[2] Atkins, P.: Physical chemistry. (1994)
[3] Benson, D.: Computational methods in Lagrangian and Eulerian hydrocodes. Comput. methods appl. Mech. eng. 99, 235 (1992) · Zbl 0763.73052
[4] Cocchi, J. -P; Saurel, S.: A Riemann problem based method for the resolution of compressible multimaterial flows. J. comput. Phys. 137, 265 (1997) · Zbl 0934.76055
[5] Davis, S.: An interface tracking method for hyperbolic systems of conservation laws. Appl. numer. Math. 10, 447 (1992) · Zbl 0766.65067
[6] Fedkiw, R.; Liu, X. -D; Osher, S.: A general technique for eliminating spurious oscillations in conservative schemes for multiphase and multispecies Euler equations. (June 1997) · Zbl 1079.76059
[7] Fedkiw, R.; Marquina, A.; Merriman, B.: An isobaric fix for the overheating problem in multimaterial compressible flows. J. comput. Phys. 148, 545 (1999) · Zbl 0933.76075
[8] R. Fedkiw, B. Merriman, R. Donat, and, S. Osher, The penultimate scheme for systems of conservation laws: Finite difference ENO with Marquina’s flux splitting, in, Progress in Numerical Solutions of Partial Differental Equations, edited by, M. Hafez, Arachon, France, July 1998. · Zbl 1028.65096
[9] Fedkiw, R.; Merriman, B.; Osher, S.: Efficient characteristic projection in upwind difference schemes for hyperbolic systems (The complementary projection method). J. comput. Phys. 141, 22 (1998) · Zbl 0932.65093
[10] Fedkiw, R.; Merriman, B.; Osher, S.: High accuracy numerical methods for thermally perfect gas flows with chemistry. J. comput. Phys. 132, 175 (1997) · Zbl 0888.76053
[11] R. Fedkiw, B. Merriman, and, S. Osher, Numerical methods for a one-dimensional interface separating compressible and incompressible flows, in, Barriers and Challenges in Computational Fluid Dynamics, edited by, V. Venkatakrishnan, M. Salas, and S. Chakravarthy, Kluwer Academic, Norwell, MA, 1998, p, 155. · Zbl 0941.76063
[12] R. Fedkiw, B. Merriman, and, S. Osher, Simplified discretization of systems of hyperbolic conservation laws containing advection equations, J. Comput. Phys, in press. · Zbl 0959.76059
[13] Gerwin, R. A.: Stability of the interface between two fluids in relative motion. Rev. modern phys. 40, 652 (1968) · Zbl 0167.25804
[14] Haas, J. F.; Sturtevant, B.: Interactions of weak shock waves with cylindrical and spherical gas inhomogeneities. J. fluid mech. 181, 41 (1987)
[15] Jenny, P.; Muller, B.; Thomann, H.: Correction of conservative Euler solvers for gas mixtures. J. comput. Phys. 132, 91 (1997) · Zbl 0879.76059
[16] G.-S. Jiang, and, D. Peng, Weighted ENO schemes for Hamilton Jacobi equations, SIAM J. Numer. Anal, in press.
[17] Jiang, G. -S; Shu, C. -W: Efficient implementation of weighted ENO schemes. J. comput. Phys. 126, 202 (1996) · Zbl 0877.65065
[18] Karni, S.: Hybrid multifluid algorithms. SIAM J. Sci. comput. 17, 1019 (1996) · Zbl 0860.76056
[19] Karni, S.: Multicomponent flow calculations by a consistent primitive algorithm. J. comput. Phys. 112, 31 (1994) · Zbl 0811.76044
[20] Leveque, R. J.: Numerical methods for conservation laws. (1992) · Zbl 0847.65053
[21] Li, X. L.; Jin, B. X.; Glimm, J.: Numerical study for the three-dimensional Rayleigh--Taylor instability through the TVD/AC scheme and parallel computation. J. comput. Phys. 126, 342 (1996) · Zbl 0858.76055
[22] X.-D. Liu, R. Fedkiw, and, S. Osher, A quasi-conservative approach to multiphase Euler equations without spurious pressure oscillations, SIAM J. Sci. Stat. Comput, in press. · Zbl 1079.76059
[23] Liu, X. -D; Osher, S.: Convex ENO high order schemes without field-by-field decomposition or staggered grids. J. comput phys. 142, 304 (1998) · Zbl 0941.65082
[24] Miles, J. W.: On the disturbed motion of a plane vortex sheet. J. fluid mech. 4, 538 (1958) · Zbl 0084.42002
[25] Mulder, W.; Osher, S.; Sethian, J. A.: Computing interface motion in compressible gas dynamics. J. comput. Phys. 100, 209 (1992) · Zbl 0758.76044
[26] Osher, S.; Sethian, J. A.: Fronts propagating with curvature dependent speed: algorithms based on Hamilton--Jacobi formulations. J. comput. Phys. 79, 121 (1988) · Zbl 0659.65132
[27] Osher, S.; Shu, C. W.: High order essentially non-oscillatory schemes for Hamilton--Jacobi equations. SIAM J. Numer. anal. 28, 902 (1991) · Zbl 0736.65066
[28] Richtmyer, R. D.: Taylor instability in shock acceleration of compressible fluids. Comm. pure appl. Math. 13, 297 (1960)
[29] Shu, C. W.: Numerical experiments on the accuracy of ENO and modified ENO schemes. J. sci. Comput. 5, 127 (1990) · Zbl 0732.65085
[30] Shu, C. W.; Osher, S.: Efficient implementation of essentially non-oscillatory shock capturing schemes, II. J. comput. Phys. 83, 32 (1989) · Zbl 0674.65061
[31] Sussman, M.; Smereka, P.; Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. comput. Phys. 114, 146 (1994) · Zbl 0808.76077
[32] Quirk, J. J.; Karni, S.: On the dynamics of a shock-bubble interaction. J. fluid mech. 318, 129 (1996) · Zbl 0877.76046
[33] Wardlaw, A.: Underwater explosion test cases. (1998)
[34] Xu, S.; Aslam, T.; Stewart, D. S.: High resolution numerical simulation of ideal and non-ideal compressible reacting flows with embedded internal boundaries. Combust. theory modeling 1, 113 (1997) · Zbl 1046.80505