<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e21" altimg="si3.svg"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>-dissipativity of the linearized explicit finite-difference scheme with a kinetic regularization for 2D and 3D gas dynamics system of equations

Злотник, А. А.; Ломоносов, Т. А.

doi:10.1016/j.aml.2019.106198

Cited by 8 publications

(8 citation statements)

References 5 publications

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“…The main items of the presented full proof have recently been described briefly in [33] (Theorem 1). Clearly, neither the specific form of A nor the specific dimension n + 1 of the involved vectors are essential in it (though the continuity of G(ξ) on D has been exploited).…”

Section: We Can Write Downmentioning

confidence: 99%

“…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]. 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%

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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: We Can Write Downmentioning

confidence: 99%

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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“…For the Cauchy problem on a uniform mesh, both necessary conditions and sufficient conditions for the L 2 -dissipativity and stability, derived recently by the spectral method in [23], are improved. For the 1D case, see also [22] and, for enlarged sufficient conditions (based on better bounds for the commutator of convective and viscous terms), [17].…”

mentioning

confidence: 99%

“…cf. [19,23], with δ (ij) being the Kronecker symbol. Here B (i) , A (ii) and Â(ij) are the matrices of the convective and viscous (regularizing) terms of the order n + 2.…”

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confidence: 99%

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Conditions for $L^2$-dissipativity of an explicit symmetric finite-difference scheme for linearized 2d and 3d gas dynamics equations with a regularization

Злотник

2023

DCDS-B

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<p style='text-indent:20px;'>We study an explicit two-level in time and symmetric in space finite-difference scheme for a linearized 2D and 3D gas dynamic system of equations with a kinetic-type regularization. For an initial-boundary value problem on any nonuniform rectangular mesh, sufficient Courant-type conditions for the <inline-formula><tex-math id="M2">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-dissipativity are derived for the first time by the energy method. For the Cauchy problem on the uniform mesh, recent both necessary conditions and sufficient conditions for the <inline-formula><tex-math id="M3">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-dissipativity in the spectral method are improved. A new form for the relaxation parameter is suggested which guarantees that the Courant-type number is uniformly bounded from above and below with respect to the mesh and the Mach number.</p>

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Prediction of the Free Jet Noise Using Quasi-gas Dynamic Equations and Acoustic Analogy

Epikhin

Kraposhin

2020

Lecture Notes in Computer Science

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L2-dissipativity of the linearized explicit finite-difference scheme with a kinetic regularization for 2D and 3D gas dynamics system of equations

Cited by 8 publications

References 5 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

Conditions for $L^2$-dissipativity of an explicit symmetric finite-difference scheme for linearized 2d and 3d gas dynamics equations with a regularization

Prediction of the Free Jet Noise Using Quasi-gas Dynamic Equations and Acoustic Analogy

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