zbMATH — the first resource for mathematics

On new spatial discretization of the multidimensional quasi-gasdynamic system of equations with nondecreasing total entropy. (English. Russian original) Zbl 1354.35121
Dokl. Math. 94, No. 1, 423-429 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 469, No. 4, 402-408 (2016).
Summary: The multidimensional quasi-gasdynamic system of equations written in the form of mass, momentum, and total energy balance equations for a perfect polytropic gas with allowance for a body force and a heat source is considered. A new conservative symmetric spatial discretization on a nonuniform rectangular grid is constructed for this system. The basic unknown functions (density, velocity, and temperature) are defined on a common grid, while the fluxes and viscous stresses, on staggered grids. The discretization is specially constructed so that the total entropy does not decrease, which is achieved by applying numerous original features.
35Q35 PDEs in connection with fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics, general
76M20 Finite difference methods applied to problems in fluid mechanics
Full Text: DOI
[1] B. N. Chetverushkin, Kinetic Schemes and Quasi-Gas Dynamic System of Equations (MAKS, Moscow, 2004; CIMNE, Barcelona, 2008). · Zbl 1217.82002
[2] T. G. Elizarova, Quasi-Gas Dynamic Equations (Nauchnyi Mir, Moscow, 2007; Springer-Verlag, Berlin, 2009). · Zbl 1169.76001
[3] Yu. V. Sheretov, Continuum Dynamics under Spatiotemporal Averaging (NITs Regulyarnaya i Khaoticheskaya Dinamika, Moscow, 2009) [in Russian]. · Zbl 1357.76005
[4] Zlotnik, A. A.; Chetverushkin, B. N., No article title, Dokl. Math., 77, 1, (2008) · Zbl 1153.76054
[5] Zlotnik, A. A., No article title, Dokl. Math., 81, 312-316, (2010) · Zbl 1387.35510
[6] Zlotnik, A. A., No article title, Mat. Model., 22, 53-64, (2010)
[7] Amosov, A. A.; Zlotnik, A. A., No article title, Sov. J. Numer. Anal. Math. Model., 2, 159-178, (1987)
[8] Fjordholm, U. S.; Mishra, S.; Tadmor, E., No article title, SIAM J. Numer. Anal., 50, 544-573, (2012) · Zbl 1252.65150
[9] Godunov, S. K.; Kulikov, I. M., No article title, Comput. Math. Math. Phys., 54, 1012-1024, (2014) · Zbl 1313.35238
[10] Mohammed, A. N.; Ismail, F., No article title, J. Sci. Comput., 63, 612-631, (2015) · Zbl 1426.76480
[11] Winters, A. R.; Gassner, G. J., No article title, J. Comput. Phys., 304, 72-108, (2016) · Zbl 1349.76407
[12] Zlotnik, A. A., No article title, Comput. Math. Math. Phys., 52, 1060-1071, (2012) · Zbl 1274.35301
[13] Gavrilin, V. A.; Zlotnik, A. A., No article title, Comput. Math. Math. Phys., 55, 264-281, (2015) · Zbl 1330.76103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.