Abstract
We consider an explicit conservative quasi-monotone difference scheme of the second order of accuracy proposed by A.P. Favorskii for the numerical solution of the equations of gas dynamics. Substantiation of the main methods and approaches underlying its construction is given.
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REFERENCES
Toro, E.F., Riemann Solvers and Numerical Methods for Fluid Dynamics, Berlin: Springer, 1999.
Kulikovskii, A.G., Pogorelov, N.V., and Semenov, A.Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii (Mathematical Issues of Numerical Solution of Hyperbolic Systems of Equations), Moscow: Fizmatlit, 2001.
Godunov, S.K., A difference method for numerical calculation of discontinuous solutions of hydrodynamics, Mat. Sb., 1959, vol. 47 (89), no. 3, pp. 271–306.
Magomedov, K.M. and Kholodov, A.S., Setochno-kharakteristicheskie chislennye metody (Grid-Characteristic Numerical Methods), Moscow: Nauka, 1988.
Favorskii, A.P., Tygliyan, M.A., Tyurina, N.N., Galanina, A.M., and Isakov, V.A., Computational modeling of the propagation of acoustic pulses in hemodynamics, Differ. Equations, 2009, vol. 45. N 8, pp. 1203–1211.
Favorskii, A.P., Tygliyan, M.A., Tyurina, N.N., Galanina, A.M., and Isakov, V.A., Computational modeling of the propagation of hemodynamic impulses, Math. Models Comput. Simul., 2010, vol. 2, no. 4, pp. 470–481.
Abakumov, M.V., Galanina, A.M., Isakov, V.A., Tyurina, N.N., Favorskii, A.P., and Khrulenko, A.B., Quasi-acoustic scheme for the Euler equations of gas dynamics, Differ. Equations, 2011, vol. 47, no. 8, pp. 1103–1109.
Isakov, V.A. and Favorskii, A.P., Quasi-acoustic scheme for gas dynamics Euler equations in the two-dimensional case, Math. Models Comput. Simul., 2013, vol. 5, no. 4, pp. 356–359.
Galanina, A.M., Isakov, V.A., Tyurina, N.N., and Favorskii, A.P., Constructive approach to numerical solution of quasi-linear advection equations, Math. Models Comput. Simul., 2014, vol. 6, no. 2, pp. 155–161.
Samarskii, A.A. and Popov, Yu.P., Raznostnye metody resheniya zadach gazovoi dinamiki (Difference Methods for Solving Problems of Gas Dynamics), Moscow: Nauka, 2004.
Courant, R., Friedrichs, K., and Lewy, H., Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann., 1928, vol. 100, no. 1, pp. 32–74.
Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow: Nauka, 1989.
Lax, P.D. and Wendroff, B., Difference schemes for hyperbolic equations with high order of accuracy, Commun. Pure Appl. Math., 1964, vol. 17, no. 3, pp. 381–398.
Rozhdestvenskii, B.L. and Yanenko, N.N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike (Systems of Quasilinear Equations and Applications to Gas Dynamics), Moscow: Nauka, 1978.
Landau, L.D. and Lifshitz, E.M., Teoreticheskaya fizika. T. 4. Gidrodinamika (Theoretical Physics. Vol. 4. Hydrodynamics), Moscow: Nauka, 1986.
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Translated by V. Potapchouck
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Abakumov, M.V., Isakov, V.A. On A.P. Favorskii’s Quasiacoustic Scheme. Diff Equat 59, 799–809 (2023). https://doi.org/10.1134/S0012266123060083
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DOI: https://doi.org/10.1134/S0012266123060083