On Conditions for <i>L</i><sup>2</sup>-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations

We deal with 2D and 3D barotropic gas dynamics system of equations with two viscous regularizations: so-called quasi-gas dynamics (QGD) and quasi-hydrodynamics (QHD) ones. The system is linearized on a constant solution with any velocity, and an explicit two-level in time and symmetric three-point i...

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Autor principal:	Alexander Zlotnik
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	barotropic gas dynamics equations regularization explicit two-level scheme dissipativity Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/57f98a7862da411e8d79e380551a3ce6
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spelling	oai:doaj.org-article:57f98a7862da411e8d79e380551a3ce62021-11-25T19:07:25ZOn Conditions for <i>L</i><sup>2</sup>-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations10.3390/sym131121842073-8994https://doaj.org/article/57f98a7862da411e8d79e380551a3ce62021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2184https://doaj.org/toc/2073-8994We deal with 2D and 3D barotropic gas dynamics system of equations with two viscous regularizations: so-called quasi-gas dynamics (QGD) and quasi-hydrodynamics (QHD) ones. The system is linearized on a constant solution with any velocity, and an explicit two-level in time and symmetric three-point in each spatial direction finite-difference scheme on the uniform rectangular mesh is considered for the linearized system. We study <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mn>2</mn></msup></semantics></math></inline-formula>-dissipativity of solutions to the Cauchy problem for this scheme by the spectral method and present a criterion in the form of a matrix inequality containing symbols of symmetric matrices of convective and regularizing terms. Analyzing these inequality and matrices, we also derive explicit sufficient conditions and necessary conditions in the Courant-type form which are rather close to each other. For the QHD regularization, such conditions are derived for the first time in 2D and 3D cases, whereas, for the QGD regularization, they improve those that have recently been obtained. Explicit formulas for a scheme parameter that guarantee taking the maximal time step are given for these conditions. An important moment is a new choice of an “average” spatial mesh step ensuring the independence of the conditions from the ratios of the spatial mesh steps and, for the QGD regularization, from the Mach number as well.Alexander ZlotnikMDPI AGarticlebarotropic gas dynamics equationsregularizationexplicit two-level schemedissipativityMathematicsQA1-939ENSymmetry, Vol 13, Iss 2184, p 2184 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	barotropic gas dynamics equations regularization explicit two-level scheme dissipativity Mathematics QA1-939
spellingShingle	barotropic gas dynamics equations regularization explicit two-level scheme dissipativity Mathematics QA1-939 Alexander Zlotnik On Conditions for <i>L</i><sup>2</sup>-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations
description	We deal with 2D and 3D barotropic gas dynamics system of equations with two viscous regularizations: so-called quasi-gas dynamics (QGD) and quasi-hydrodynamics (QHD) ones. The system is linearized on a constant solution with any velocity, and an explicit two-level in time and symmetric three-point in each spatial direction finite-difference scheme on the uniform rectangular mesh is considered for the linearized system. We study <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mn>2</mn></msup></semantics></math></inline-formula>-dissipativity of solutions to the Cauchy problem for this scheme by the spectral method and present a criterion in the form of a matrix inequality containing symbols of symmetric matrices of convective and regularizing terms. Analyzing these inequality and matrices, we also derive explicit sufficient conditions and necessary conditions in the Courant-type form which are rather close to each other. For the QHD regularization, such conditions are derived for the first time in 2D and 3D cases, whereas, for the QGD regularization, they improve those that have recently been obtained. Explicit formulas for a scheme parameter that guarantee taking the maximal time step are given for these conditions. An important moment is a new choice of an “average” spatial mesh step ensuring the independence of the conditions from the ratios of the spatial mesh steps and, for the QGD regularization, from the Mach number as well.
format	article
author	Alexander Zlotnik
author_facet	Alexander Zlotnik
author_sort	Alexander Zlotnik
title	On Conditions for <i>L</i><sup>2</sup>-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations
title_short	On Conditions for <i>L</i><sup>2</sup>-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations
title_full	On Conditions for <i>L</i><sup>2</sup>-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations
title_fullStr	On Conditions for <i>L</i><sup>2</sup>-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations
title_full_unstemmed	On Conditions for <i>L</i><sup>2</sup>-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations
title_sort	on conditions for <i>l</i><sup>2</sup>-dissipativity of an explicit finite-difference scheme for linearized 2d and 3d barotropic gas dynamics system of equations with regularizations
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/57f98a7862da411e8d79e380551a3ce6
work_keys_str_mv	AT alexanderzlotnik onconditionsforilisup2supdissipativityofanexplicitfinitedifferenceschemeforlinearized2dand3dbarotropicgasdynamicssystemofequationswithregularizations
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On Conditions for <i>L</i><sup>2</sup>-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations

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