Summary
Two schemes that are designed to capture contact surface sharply are examined in this study. The first one is an overset mesh method in which a submesh system moves on the background Cartesian mesh system and follows the contact surface. The other scheme is a fully conservative Eulerian scheme that introduces two inert gases to identify the coexisting region where two gases coexist in a computational cell. The numerical flux function at the boundary of coexisting region is then modified by extrapolation. The computed results for the Richtmyer-Meshkov instability problem indicate that these two schemes can capture contact surface quite sharply and accurately.
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References
Hirt, C.W., Amsden, A.A., and Cook, J.L., “An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds,” Journal of Computational Physics, Vol. 44, 1984, pp. 227–253.
Baltrusaitis, R.M., Gittings, M.L., Weaver, R.P., Benjamin, R.F., and Budzinski, J.M., “Simulation of shock-generated instabilities,” Physics of Fluids, Vol. 8, 1996, pp. 2471–2483.
Yee, H. C., “A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods,” NASA TM-101088, 1989.
Boris, J. P., and Book, D. L., “Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works,” Journal of Computational Physics, Vol. 11, 1973, pp. 38–69.
Colella, P., and Woodward, P. R., “The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations,” Journal of Computational Physics, Vol. 54, 1984, pp. 174–201.
Osher, S., and Sethian, J.A., “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” Journal of Computational Physics, Vol. 79, 1988, pp. 12–49.
Chakravarthy, S. R., and Osher, S., “Numerical Experiments with the Osher Upwind Scheme for the Euler Equations,” AIAA Journal, Vol. 21, 1983, pp. 1241–1248.
Van Leer, B., “Towards the Ultimate Conservation Difference Scheme V, A Second-Order Sequel to Godunov’s Method,” Journal of Computational Physics, Vol. 32, 1979, pp. 101–136.
Sawada, K., Ohnishi, N., Baba, H., and Nagatomo, H., “Comparative Study of Contact Surface Capturing Scheme,” AIAA Paper 2003-4117, 2003.
Wada, Y., and Liou, M.-S., “A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities,” NASA TM-106452, 1994.
Sod, G. A., “A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws,” 0Journal of Computational Physics, Vol. 27, 1978, pp. 1–31.
Baba, H., “Study of Computational Fluid Dynamics Method for Solving Flow-field Involving Contact Surfaces,” Master Thesis, Tohoku University, 2002. in Japanese
Richtmyer, R. D., “Taylor Instability in Shock Acceleration of Compressible Fluids,” Communications on Pure and Applied Mathematics, Vol. 13, 1960, pp. 297–319.
Meshkov, E. E., “Instability of the Interface of Two Gases Accelerated by a Shock Wave,” Fluid Dynamics / Academy of Sciences USSR, Vol. 4, 1969, pp. 101–104.
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Sawada, K., Ohnishi, N. (2005). Numerical Attempts of Capturing Contact Surface. In: Fujii, K., Nakahashi, K., Obayashi, S., Komurasaki, S. (eds) New Developments in Computational Fluid Dynamics. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 90. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31261-7_8
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DOI: https://doi.org/10.1007/3-540-31261-7_8
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