L2-Dissipativity Criteria for Linearized Explicit Finite Difference Schemes for Regularization of One-Dimensional Gas Dynamics Equations

Ломоносов, Т. А.

doi:10.1007/s10958-019-04639-6

Cited by 3 publications

(1 citation statement)

References 6 publications

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“…We also include the complete proof of the formula for the norm of the level-to-level transition operator in terms of the eigenvalues of its symmetrized symbol that is essential for the spectral technique; the main items of its proof have recently been presented in [33]. Importantly, the technique is general enough and applicable for various schemes, other regularizations (for example, see in [34]) and in more general or different statements of the equations, and some such studies are planned for the near future.…”

Section: Introductionmentioning

confidence: 99%

On Conditions for L2-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations

Злотник

2021

Symmetry

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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 L2-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.

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Section: Introductionmentioning

confidence: 99%

On Conditions for L2-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations

Злотник

2021

Symmetry

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On L2-Dissipativity of a Linearized Scheme on Staggered Meshes with a Regularization for 1D Barotropic Gas Dynamics Equations

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Ломоносов²

2022

Comput. Math. and Math. Phys.

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On L<sup>2</sup>-dissipativity of a linearized difference scheme on staggered meshes with a quasi-hydrodynamic regularization for 1D barotropic gas dynamics equations

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Ломоносов

2021

KIAM Prepr.

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We study an explicit two-level finite difference scheme on staggered meshes, with a quasi-hydrodynamic regularization, for 1D barotropic gas dynamics equations. We derive necessary conditions and sufficient conditions close to each other for L<sup>2</sup>-dissipativity of solutions to the Cauchy problem for its linearization on a constant solution, for any background Mach number M. We apply the spectral approach and analyze matrix inequalities containing symbols of symmetric matrices of convective and regularizing terms. We consider the cases where either the artificial viscosity coefficient or the physical viscosity one is used. A comparison with the spectral von Neumann condition is also given for M=0.

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L2-Dissipativity Criteria for Linearized Explicit Finite Difference Schemes for Regularization of One-Dimensional Gas Dynamics Equations

Cited by 3 publications

References 6 publications

On Conditions for L2-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations

On Conditions for L2-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations

On L2-Dissipativity of a Linearized Scheme on Staggered Meshes with a Regularization for 1D Barotropic Gas Dynamics Equations

On L<sup>2</sup>-dissipativity of a linearized difference scheme on staggered meshes with a quasi-hydrodynamic regularization for 1D barotropic gas dynamics equations

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