Conditions for L2-Dissipativity of Linearized Explicit Difference Schemes with Regularization for 1D Barotropic Gas Dynamics Equations

Злотник, А. А.; Ломоносов, Т. А.

doi:10.1134/s0965542519030151

Cited by 14 publications

(10 citation statements)

References 10 publications

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“…However, as a rule, this is more adequate for the entropy dissipative QGD-discretizations but overestimates the acceptable time step for the standard-type QGD-schemes. Similar conclusions follow from [23] in the simpler barotropic case.…”

Section: Computations Of the Riemann Problem And Comparison Of Schemessupporting

confidence: 80%

“…In some tests, the simplified schemes A 1 and A 2 are significantly inferior to the scheme A and thus such simplifications are not always justified. where M = |u * |/c s * and c s * = γ(γ − 1)ε * are the background Mach number and sound velocity as well as To analyze the quality of numerical solutions, we applied (similarly to [23]) the deviation of their relative variation from 1 at the time moment t = t f in :…”

Section: Computations Of the Riemann Problem And Comparison Of Schemesmentioning

confidence: 99%

See 1 more Smart Citation

Verification of an Entropy Dissipative QGD-Scheme

Злотник

Ломоносов

2019

Mathematical Modelling and Analysis

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An entropy dissipative spatial discretization has recently been constructed for the multidimensional gas dynamics equations based on their preliminary parabolic quasi-gasdynamic (QGD) regularization. In this paper, an explicit finite-difference scheme with such a discretization is verified on several versions of the 1D Riemann problem, both well-known in the literature and new. The scheme is compared with the previously constructed QGD-schemes and its merits are noticed. Practical convergence rates in the mesh L1-norm are computed. We also analyze the practical relevance in the nonlinear statement as the Mach number grows of recently derived necessary conditions for L2-dissipativity of the Cauchy problem for a linearized QGD-scheme.

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Section: Computations Of the Riemann Problem And Comparison Of Schemessupporting

confidence: 80%

Section: Computations Of the Riemann Problem And Comparison Of Schemesmentioning

confidence: 99%

Verification of an Entropy Dissipative QGD-Scheme

Злотник

Ломоносов

2019

Mathematical Modelling and Analysis

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“…The regularization parameter is associated with h and is calculated as τ = 0.5h/c s . The stability issue in the linearized statement for the considered type of the regularization and approximation in time has recently been studied in detail in 1D and multiD cases in the one-component statement in [28,29]. Notice that we do not apply any regularization of the viscosity coefficient contrary to the usual QHD-approach.…”

Section: Numerical Experimentsmentioning

confidence: 99%

An Energy Dissipative Spatial Discretization for the Regularized Compressible Navier-Stokes-Cahn-Hilliard System of Equations

Balashov

Злотник

2020

Mathematical Modelling and Analysis

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We consider the regularized 3D Navier-Stokes-Cahn-Hilliard equations describing isothermal flows of viscous compressible two-component fluids with interphase effects. We construct for them a new energy dissipative finite-difference discretization in space, i.e., with the non-increasing total energy in time. This property is preserved in the absence of a regularization. In addition, the discretization is well-balanced for equilibrium flows and the potential body force. The sought total density, mixture velocity and concentration of one of the components are defined at nodes of one and the same grid. The results of computer simulation of several 2D test problems are presented. They demonstrate advantages of the constructed discretization including the absence of the so-called parasitic currents.

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“…µ = µ S ≡ const. Now equation (37) means that equation (35) holds whereas formula (29) leads to equation (36).…”

Section: 2mentioning

confidence: 99%

“…They can be considered as numerical regularizers allowing one to apply conditionally stable explicit in time and central finite-difference approximations in space which are convenient and promising in modern parallel computations. A linearized dissipativity analysis of such schemes for 1D and multi-D one-component barotropic gas equations has recently been accomplished in [37,38]. Though all the theoretical results in this paper are valid uniformly in τ ≥ 0, numerical experiments demonstrate that, in the absence of regularization (i.e., for τ = 0), the time step has to be reduced by several orders of magnitude to get adequate solutions, and thus the simulation time increases unacceptably.…”

mentioning

confidence: 99%

An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier–Stokes–Cahn–Hilliard equations

Balashov¹,

Злотник²

2020

Journal of Computational Dynamics

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We consider the initial-boundary value problem for the 3D regularized compressible isothermal Navier-Stokes-Cahn-Hilliard equations describing flows of a two-component two-phase mixture taking into account capillary effects. We construct a new numerical semi-discrete finite-difference method using staggered meshes for the main unknown functions. The method allows one to improve qualitatively the computational flow dynamics by eliminating the so-called parasitic currents and keeping the component concentration inside the physically reasonable range (0, 1). This is achieved, first, by discretizing the non-divergent potential form of terms responsible for the capillary effects and establishing the dissipativity of the discrete full energy. Second, a logarithmic (or the Flory-Huggins potential) form for the non-convex bulk free energy is used. The regularization of equations is accomplished to increase essentially the time step of the explicit discretization in time. We include 3D numerical results for two typical problems that confirm the theoretical predictions.

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Conditions for L2-Dissipativity of Linearized Explicit Difference Schemes with Regularization for 1D Barotropic Gas Dynamics Equations

Cited by 14 publications

References 10 publications

Verification of an Entropy Dissipative QGD-Scheme

Verification of an Entropy Dissipative QGD-Scheme

An Energy Dissipative Spatial Discretization for the Regularized Compressible Navier-Stokes-Cahn-Hilliard System of Equations

An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier–Stokes–Cahn–Hilliard equations

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