On L2-Dissipativity of a Linearized Explicit Finite-Difference Scheme with Quasi-Gasdynamic Regularization for the Barotropic Gas Dynamics System of Equations

Злотник, А. А.; Ломоносов, Т. А.

doi:10.1134/s1064562420030229

Cited by 8 publications

(6 citation statements)

References 11 publications

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“…For the QHD regularization, these 2D and 3D results are derived for the first time and, for the QGD regularization, they improve those that have recently been obtained in [29]. Previously, the L 2 -dissipativity analysis of similar schemes in the much simpler 1D barotropic case was accomplished for zero and any Mach number in [30][31][32], respectively.…”

Section: Introductionsupporting

confidence: 66%

“…serve as necessary conditions as well. For = 1, this was proved in ( [29], Theorem 2) by reducing to the 1D case and, for = 0, this is proved in the same way (recall that the 1D case was previously studied in [32]). The form of matrices A (ij) , i = j, is inessential in this proof.…”

Section: We Can Write Downmentioning

confidence: 60%

“…Proof. For = 1, the result was proven in ( [29], Lemma 1). For = 0, by virtue of Formulas ( 5) and ( 6) for the matrices A (ij) together with…”

Section: An Analysis Of the L 2 -Dissipativity Of The Schemementioning

confidence: 82%

“…The first of these inequalities is a consequence of the inequality (tr Q)v 2 0 + 2v 0 M T Qv + M T QM|v| 2 0 that follows from the estimates (already used in [29])…”

Section: We Can Write Downmentioning

confidence: 93%

“…Previously, the L 2 -dissipativity analysis of similar schemes in the much simpler 1D barotropic case was accomplished for zero and any Mach number in [30][31][32], respectively. In this paper, we base on the papers in [29,32] and aim to develop further their technique. 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].…”

Section: Introductionmentioning

confidence: 99%

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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: Introductionsupporting

confidence: 66%

Section: We Can Write Downmentioning

confidence: 60%

“…Proof. For = 1, the result was proven in ( [29], Lemma 1). For = 0, by virtue of Formulas ( 5) and ( 6) for the matrices A (ij) together with…”

Section: An Analysis Of the L 2 -Dissipativity Of The Schemementioning

confidence: 82%

“…The first of these inequalities is a consequence of the inequality (tr Q)v 2 0 + 2v 0 M T Qv + M T QM|v| 2 0 that follows from the estimates (already used in [29])…”

Section: We Can Write Downmentioning

confidence: 93%