Abstract
The ability of previously proposed modifications of Godunov’s scheme to develop physically justified numerical solutions of the equations of inviscid gas dynamics is tested. Modifications constructed using the approach proposed by Kolgan to improve the accuracy of solutions in spatial variables are considered. The problems of a coaxial supersonic flow around a semi-infinite rectangle and a circular cylinder are solved. The calculations are performed on a uniform rectangular grid. It is shown that the numerical solution can correspond to both a steady and pulsating flow with different shapes of shock waves in front of the end wall, depending on the viscosity of the numerical scheme and the initial parameter distribution.
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REFERENCES
Godunov, S.K., Finite method for calculating discontinuous solutions of hydrodynamic equations, Mat. Sb., 1959, vol. 47 (89), no. 3, pp. 271–306.
Godunov, S.K., Zabrodin, A.V., Ivanov, M.Ya., Kraiko, A.N., and Prokopov, G.P., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki (Numerical Simulation of Multidimensional Gas Dynamics Problems), Moscow: Nauka, 1976.
Kolgan, V.P., The way to apply principle of derivative minimal value for generating finite-element schemes for calculating discontinuous solutions of gas dynamics, Uch. Zap. TsAGI, 1972, vol. 3, no. 6, pp. 68–77.
Kolgan, V.P., Finite element scheme for calculating 2D discontinuous solutions of nonstationary gas dynamics, Uch. Zap. TsAGI, 1975, vol. 6, no. 1, pp. 9–14.
Tillyaeva, N.I., The way for generalizing modified S.K. Godunov scheme at arbitrary irregular grids, Uch. Zap. TsAGI, 1986, vol. 17, no. 2, pp. 18–26.
Harten, A., Lax, P.D., and van Leer, B., On upstreaming differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev., 1983, vol. 25, pp. 35–61.
Roe, P.L., Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 1981, vol. 43, pp. 357–372.
Osher, S. and Chakravarthy, S.R., Upwind schemes and boundary conditions with applications to Euler equations in general geometries, J. Comput. Phys., 1983, vol. 50, pp. 447–481.
Schulz-Rinne, C.W., Collins, J.P., and Glaz, H.M., Numerical solution of the Riemann problem for two-dimensional gas dynamics, SIAM J. Sci. Comput., 1993, vol. 14, pp. 1394–1414.
Toro, B.F. and Chakraborty, A., Development of an approximate Riemann solver for the steady supersonic Euler equations, Aeronaut. J., 1994, vol. 98, pp. 325–339.
Vasil’ev, E.I., W-modification for S.K. Godunov method and its application to 2D nonstationary dusted gas flows, Zh. Vychisl. Mat. Mat. Fiz., 1996, vol. 36, no. 1, pp. 122–135.
Tunik, Yu.V., Instability of contact surface in cylindrical explosive waves, Fluid Mech.: Open Access, 2017, vol. 4, no. 4. https://doi.org/10.4172/2476-2296.1000168
Belotserkovskii, O.M. and Davydov, Yu.M., Metod krupnykh chastits v gazovoi dinamike (Large-Particle Method in Gas Dynamics), Moscow: Nauka, Glavnaya redaktsiya fiziko-matematicheskoi literatury, 1982.
An Album of Fluid Motion, Van Dyke, M., Ed., Parabolic Press, 1982.
ACKNOWLEDMENTS
This work was performed using the “Lomonosov” supercomputer of the Moscow State University.
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Translated by E. Chernokozhin
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Tunik, Y.V. Problems of Numerical Simulation Based on Some Modifications of Godunov’s Scheme. Fluid Dyn 57 (Suppl 1), S75–S83 (2022). https://doi.org/10.1134/S0015462822601334
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DOI: https://doi.org/10.1134/S0015462822601334