Abstract:
Explicit two-level in time and symmetric in space difference schemes constructed by approximating the 1D barotropic quasi-gas-/quasi-hydrodynamic systems of equations are studied. The schemes are linearized about a constant solution with a nonzero velocity, and, for them, necessary and sufficient conditions for the ${{L}^{2}}$ -dissipativity of solutions to the Cauchy problem are derived depending on the Mach number. These conditions differ from one another by at most twice. The results substantially develop the ones known for the linearized
Lax–Wendroff scheme. Numerical experiments are performed to analyze the applicability of the found conditions in the nonlinear formulation to several schemes for different Mach numbers.
Key words:
equations of one-dimensional barotropic gas dynamics, quasi-gasdynamic system of equations, explicit two-level difference schemes, stability, $L^2$-dissipativity.
Citation:
A. A. Zlotnik, T. A. Lomonosov, “Conditions for $L^2$-dissipativity of linearized explicit difference schemes with regularization for $\mathrm{1D}$ barotropic gas dynamics equations”, Zh. Vychisl. Mat. Mat. Fiz., 59:3 (2019), 481–493; Comput. Math. Math. Phys., 59:3 (2019), 452–464
This publication is cited in the following 15 articles:
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A. A. Zlotnik, T. A. Lomonosov, “On $L^2$-dissipativity of a linearized scheme on staggered meshes with a regularization for 1D barotropic gas dynamics equations”, Comput. Math. Math. Phys., 62:12 (2022), 1817–1837
A. A. Zlotnik, T. A. Lomonosov, “$L^2$-dissipativity of finite-difference schemes for $\mathrm{1D}$ regularized barotropic gas dynamics equations at small Mach numbers”, Math. Models Comput. Simul., 13:6 (2021), 1097–1108
A. A. Zlotnik, T. A. Lomonosov, “O $L^2$-dissipativnosti linearizovannoi raznostnoi skhemy na raznesennykh setkakh s kvazigidrodinamicheskoi regulyarizatsiei dlya $\mathrm{1D}$ barotropnykh uravnenii dvizheniya gaza”, Preprinty IPM im. M. V. Keldysha, 2021, 072, 27 pp.
V. Balashov, “A regularized isothermal phase-field model of two-phase solid-fluid mixture and its spatial dissipative discretization”, Russ. J. Numer. Anal. Math. Model, 36:4 (2021), 197–217
A. Zlotnik, “On conditions for $L^2$-dissipativity of an explicit finite-difference scheme for linearized 2D and 3D barotropic gas dynamics system of equations with regularizations”, Symmetry-Basel, 13:11 (2021), 2184
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
V. Balashov, A. Zlotnik, “An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier-Stokes-Cahn-Hilliard equations”, J. Comput. Dynam., 7:2 (2020), 291–312
A. A. Zlotnik, T. A. Lomonosov, “On $L^2$-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations”, Dokl. Math.
101, no. 3, 2020, 198–204
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
Alexander Zlotnik, Springer Proceedings in Mathematics & Statistics, 333, Differential and Difference Equations with Applications, 2020, 53
T. A. Lomonosov, “L2-Dissipativity Criteria for Linearized Explicit Finite Difference Schemes for Regularization of One-Dimensional Gas Dynamics Equations”, J Math Sci, 244:4 (2020), 649
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
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