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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 2, Pages 301–317 (Mi zvmmf10346)  

This article is cited in 17 scientific papers (total in 17 papers)

On conservative spatial discretizations of the barotropic quasi-gasdynamic system of equations with a potential body force

A. A. Zlotnik

Department of Mathematics, Faculty of Economics Sciences, National Research University Higher School of Economics, Myasnitskaya ul. 20, Moscow, 101000, Russia

Abstract: A multidimensional barotropic quasi-gasdynamic system of equations in the form of mass and momentum conservation laws with a general gas equation of state $p=p(\rho)$ with $p'(\rho)>0$ and a potential body force is considered. For this system, two new symmetric spatial discretizations on nonuniform rectangular grids are constructed (in which the density and velocity are defined on the basic grid, while the components of the regularized mass flux and the viscous stress tensor are defined on staggered grids). These discretizations involve nonstandard approximations for $\nabla p(\rho)$, $\mathrm{div}(\rho\mathbf{u})$, and $\rho$. As a result, a discrete total mass conservation law and a discrete energy inequality guaranteeing that the total energy does not grow with time can be derived. Importantly, these discretizations have the additional property of being well-balanced for equilibrium solutions. Another conservative discretization is discussed in which all mass flux components and viscous stresses are defined on the same grid. For the simpler barotropic quasi-hydrodynamic system of equations, the corresponding simplifications of the constructed discretizations have similar properties.

Key words: viscous compressible Navier–Stokes equations, quasi-gasdynamic system of equations, potential body force, spatial discretization, energy balance equation, well balanced property.

Funding Agency Grant Number
National Research University Higher School of Economics 15-09-0266
Russian Foundation for Basic Research 13-01-00703_а
14-01-90009-Бел_а


DOI: https://doi.org/10.7868/S0044466916020186

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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:2, 303–319

Bibliographic databases:

UDC: 517.958:533.7
Received: 02.06.2015

Citation: A. A. Zlotnik, “On conservative spatial discretizations of the barotropic quasi-gasdynamic system of equations with a potential body force”, Zh. Vychisl. Mat. Mat. Fiz., 56:2 (2016), 301–317; Comput. Math. Math. Phys., 56:2 (2016), 303–319

Citation in format AMSBIB
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    6. T. G. Elizarova, A. A. Zlotnik, M. A. Istomina, “O dvumernom chislennom KGD modelirovanii spiralno-vikhrevykh struktur v akkretsionnykh gazovykh diskakh”, Preprinty IPM im. M. V. Keldysha, 2017, 001, 30 pp.  mathnet  crossref
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    9. V. A. Balashov, V. E. Borisov, “Algoritm rascheta trekhmernykh techenii umerenno-razrezhennogo gaza v oblastyakh s vokselnoi geometriei”, Preprinty IPM im. M. V. Keldysha, 2017, 099, 24 pp.  mathnet  crossref
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    11. V. A. Balashov, “Direct numerical simulation of moderately rarefied gas flow within two-dimensional artificial porous media”, Math. Models Comput. Simul., 10:4 (2018), 483–493  mathnet  crossref  elib
    12. A. Zlotnik, “On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier–Stokes equations in polar coordinates”, Russ. J. Numer. Anal. Math. Model, 33:3 (2018), 199–210  crossref  mathscinet  zmath  isi
    13. V. A. Balashov, “Pryamoe modelirovanie mikrotechenii umerenno-razrezhennogo gaza v obraztsakh gornykh porod”, Matem. modelirovanie, 30:9 (2018), 3–20  mathnet
    14. T. G. Elizarova, A. V. Ivanov, “Regularized equations for numerical simulation of flows in the two-layer shallow water approximation”, Comput. Math. Math. Phys., 58:5 (2018), 714–734  mathnet  crossref  crossref  isi  elib
    15. A. Zlotnik, T. Lomonosov, “On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations”, Differential and Difference Equations With Applications, Springer Proceedings in Mathematics & Statistics, 230, eds. S. Pinelas, T. Caraballo, P. Kloeden, J. Graef, Springer, 2018, 635–647  crossref  mathscinet  zmath  isi  scopus
    16. Zlotnik A., “On l-2-Dissipativity of Linearized Explicit Finite-Difference Schemes With a Regularization on a Non-Uniform Spatial Mesh For the 1D Gas Dynamics Equations”, Appl. Math. Lett., 92 (2019), 115–120  crossref  mathscinet  zmath  isi  scopus
    17. Balashov V. Savenkov E. Zlotnik A., “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  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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