Robust numerical schemes for Two-Fluid Ten-Moment plasma flow equations

Meena, Asha Kumari; Kumar, Harish

doi:10.1007/s00033-018-1061-3

Cited by 6 publications

(5 citation statements)

References 25 publications

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“…Expression (25) clearly shows that if f is entropy stable then together with the compact (or periodic) boundary condition the scheme is globally entropy stable.…”

Section: Theorem 31 ([8]mentioning

confidence: 99%

“…In several fluid and plasma flow applications assumptions of the local thermodynamic equilibrium do not hold (see [14,29,5,28,19,25]). Due to this, the simulations of such flows using the scalar description of the pressure (used most commonly in Euler equations of compressible fluid flows) is not accurate and instead a tonsorial pressure (and hence temperature) is needed.…”

Section: Introductionmentioning

confidence: 99%

“…Due to this, the simulations of such flows using the scalar description of the pressure (used most commonly in Euler equations of compressible fluid flows) is not accurate and instead a tonsorial pressure (and hence temperature) is needed. One such model is ten-moment Gaussian closure equations (see [1,2,26,31,24,25,21,22]). It is one of the simplest fluid model which consider pressure as tensor.…”

Section: Introductionmentioning

confidence: 99%

“…In [1,2] Berthon has developed first-order entropy stable and first-order positivity preserving schemes. The positivity preserving schemes are then extended to higher-order finite volume, DG, and WENO schemes by Meena et al in [26,25,27]. Furthermore, in [24], authors have proposed a well-balanced scheme for a potential type source terms.…”

Section: Introductionmentioning

confidence: 99%

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Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations

Biswas,

Kumar,

Yadav

2020

Preprint

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In this article, we propose high order discontinuous Galerkin entropy stable schemes for ten-moment Gaussian closure equations, which is based on the suitable quadrature rules (see [8]). The key components of the proposed method are the use of an entropy conservative numerical flux [31] in each cell and a suitable entropy stable numerical flux at the cell edges. This is then used in the entropy stable DG framework of [8] to obtain entropy stability of the semi-discrete scheme. We also extend these schemes to a source term that models plasma laser interaction. For the time discretization, we use strong stability preserving schemes. The proposed schemes are then tested on several test cases to demonstrate stability, accuracy, and robustness.

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“…Expression (25) clearly shows that if f is entropy stable then together with the compact (or periodic) boundary condition the scheme is globally entropy stable.…”

Section: Theorem 31 ([8]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations

Biswas,

Kumar,

Yadav

2020

Preprint

Self Cite

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show abstract

“…However, RMHD has limitations when modeling several astrophysical systems, like pulsar, gamma-ray burst, etc., see [12] for a detailed discussion. Following the development of non-relativistic two-fluid plasma flow equations [13], [14], [15], [16], [17], [18], [19], several authors have considered an analogous relativistic two-fluid plasma flow equations [20], [21], [22], [23], [24]. Two-fluid relativistic plasma flow equations describe each fluid (ion and electron) in plasma using the equations of special relativistic hydrodynamics (RHD).…”

Section: Introductionmentioning

confidence: 99%

High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations

Bhoriya¹,

Kumar²,

Chandrashekar³

2022

Preprint

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In this article, we propose high-order finite-difference entropy stable schemes for the twofluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux components. The first two components describe the ion and electron flows, which are modeled using the relativistic hydrodynamics equation. The third component is Maxwell's equations, which are linear systems. The coupling of the ion and electron flows, and electromagnetic fields is via source terms only. Furthermore, we also show that the source terms do not affect the entropy evolution. To design semi-discrete entropy stable schemes, we extend the RHD entropy stable schemes in [1] to three dimensions. This is then coupled with entropy stable discretization of the Maxwell's equations. Finally, we use SSP-RK schemes to discretize in time. We also propose ARK-IMEX schemes to treat the stiff source terms; the resulting nonlinear set of algebraic equations is local (at each discretization point). These equations are solved using the Newton's Method, which results in an efficient method. The proposed schemes are then tested using various test problems to demonstrate their stability, accuracy and efficiency.

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Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations

Biswas

Kumar

Yadav

2021

Journal of Computational Physics

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Robust numerical schemes for Two-Fluid Ten-Moment plasma flow equations

Cited by 6 publications

References 25 publications

Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations

Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations

High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations

Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations

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