Abstract:
The multidimensional quasi-gasdynamic system 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 of these equations on a nonuniform rectangular grid is constructed (with the basic unknown functions—density, velocity, and temperature—defined on a common grid and with fluxes and viscous stresses defined on staggered grids). Primary attention is given to the analysis of entropy behavior: the discretization is specially constructed so that the total entropy does not decrease. This is achieved via a substantial revision of the standard discretization and applying numerous original features. A simplification of the constructed discretization serves as a conservative discretization with nondecreasing total entropy for the simpler quasi-hydrodynamic system of equations. In the absence of regularizing terms, the results also hold for the Navier–Stokes equations of a viscous compressible heat-conducting gas.
Key words:
Navier-Stokes equations for viscous compressible heat-conducting gases, quasi-gasdynamic system of equations, spatial discretization, conservativeness, law of nondecreasing entropy.
Citation:
A. A. Zlotnik, “Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations”, Zh. Vychisl. Mat. Mat. Fiz., 57:4 (2017), 710–729; Comput. Math. Math. Phys., 57:4 (2017), 706–725
This publication is cited in the following 25 articles:
Vladislav Balashov, Evgeny Savenkov, Aleksey Khlyupin, Kirill M. Gerke, “Two-phase regularized phase-field density gradient Navier–Stokes based flow model: Tuning for microfluidic and digital core applications”, Journal of Computational Physics, 2024, 113554
Y. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method in conservative variables for three-dimensional Euler equations”, Math. Models Comput. Simul., 16:6 (2024), 843–852
Alexander Zlotnik, “Conditions for L2-dissipativity of an explicit symmetric finite-difference scheme for linearized 2d and 3d gas dynamics equations with a regularization”, DCDS-B, 28:3 (2023), 1571
Alexander Zlotnik, Timofey Lomonosov, “On Regularized Systems of Equations for Gas Mixture Dynamics with New Regularizing Velocities and Diffusion Fluxes”, Entropy, 25:1 (2023), 158
I. M. Kulikov, “Using piecewise parabolic reconstruction of physical variables in the Rusanov solver. I. The special relativistic hydrodynamics equations”, J. Appl. Industr. Math., 17:4 (2023), 737–749
Yu. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method for two-dimensional Euler equations in triangulated domains”, Math. Models Comput. Simul., 15:5 (2023), 781–791
I. M. Kulikov, “Using a Combination of Godunov and Rusanov Solvers Based on the Piecewise Parabolic Reconstruction of Primitive Variables for Numerical Simulation of Supernovae Ia Type Explosion”, Lobachevskii J Math, 43:6 (2022), 1545
Alexander Zlotnik, Anna Fedchenko, Timofey Lomonosov, “Entropy Correct Spatial Discretizations for 1D Regularized Systems of Equations for Gas Mixture Dynamics”, Symmetry, 14:10 (2022), 2171
M. D. Bragin, Y. A. Kriksin, V. F. Tishkin, “Entropy stable discontinuous Galerkin method for two-dimensional Euler equations”, Math. Models Comput. Simul., 13:5 (2021), 897–906
M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Entropic regularization of the discontinuous Galerkin method in conservative variables for two-dimensional Euler equations”, Math. Models Comput. Simul., 14:4 (2022), 578–589
V. Balashov, A. Zlotnik, “On a new spatial discretization for a regularized 3D compressible isothermal Navier-Stokes-Cahn-Hilliard system of equations with boundary conditions”, J. Sci. Comput., 86:3 (2021), 33
V. A. Balashov, “Dissipative spatial discretization of a phase field model of multiphase isothermal fluid flow”, Comput. Math. Appl., 90 (2021), 112–124
N. Cao, X. Miao, J. Zhang, “Spatial intelligent decision system based on multidimensional network theory”, J. Intell. Fuzzy Syst., 40:4 (2021), 6137–6149
M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Discontinuous Galerkin method with entropic slope limiter for Euler equations”, Math. Models Comput. Simul., 12:5 (2020), 824–833
Y. A. Kriksin, V. F. Tishkin, “Entropy stable discontinuous Galerkin method for Euler equations using non-conservative variables”, Math. Models Comput. Simul., 13:3 (2021), 416–425
V. Balashov, A. Zlotnik, “An energy dissipative spatial discretization for the regularized compressible Navier-Stokes-Cahn-Hilliard system of equations”, Math. Model. Anal., 25:1 (2020), 110–129
M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Verifikatsiya odnogo metoda entropiinoi regulyarizatsii razryvnykh skhem Galerkina dlya uravnenii giperbolicheskogo tipa”, Preprinty IPM im. M. V. Keldysha, 2019, 018, 25 pp.
V. Balashov, E. Savenkov, A. Zlotnik, “Numerical method for 3D two-component isothermal compressible flows with application to digital rock physics”, Russ. J. Numer. Anal. Math. Model, 34:1 (2019), 1–13
A. Zlotnik, T. Lomonosov, “Verification of an entropy dissipative QGD-scheme for the 1D gas dynamics equations”, Math. Model. Anal., 24:2 (2019), 179–194
M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Obespechenie entropiinoi ustoichivosti razryvnogo metoda Galerkina v gazodinamicheskikh zadachakh”, Preprinty IPM im. M. V. Keldysha, 2019, 051, 22 pp.
Citation in format AMSBIB
Contact us: