Smoothed MHD equations for numerical simulations of ideal quasi-neutral gas dynamic flows

Попов, М. В.; Елизарова, Т. Г.

doi:10.1016/j.cpc.2015.07.003

Cited by 11 publications

(6 citation statements)

References 38 publications

(69 reference statements)

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“…The three‐dimensional blast wave problem can be built as the direct extension of what presented in the previous paragraph, see also Reference 89, after re‐defining the three‐dimensional radial position

r = \sqrt{x^{2} + y^{2} + z^{2}}

. The computational domain is a three‐dimensional periodic box

(x, y, z) \in {[- 0.55, 0.55]}^{3}

that is discretized with a mesh resolution of

Δ x = Δ y = Δ z = 1 / 150

.…”

Section: Numerical Validationmentioning

confidence: 99%

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A novel structure preserving semi‐implicit finite volume method for viscous and resistive magnetohydrodynamics

Fambri

2021

Numerical Methods in Fluids

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In this work we introduce a novel semi‐implicit structure‐preserving finite‐volume/finite‐difference scheme for the viscous and resistive equations of magneto‐hydrodynamics (VRMHD) based on an appropriate 3‐split of the governing PDE system, which is decomposed into a first convective subsystem, a second subsystem involving the coupling of the velocity field with the magnetic field, and a third subsystem involving the pressure‐velocity coupling. The nonlinear convective terms are discretized explicitly, while the remaining two subsystems accounting for the Alfvén waves and the magneto‐acoustic waves are treated implicitly. Thanks to this, the final algorithm is at least formally constrained only by a mild CFL stability condition depending on the velocity field of the pure hydrodynamic convection. To preserve the divergence‐free constraint of the magnetic field exactly at the discrete level, a proper set of overlapping dual (staggered) meshes is employed. The resulting linear algebraic systems are shown to be symmetric and therefore can be solved by means of an efficient standard matrix‐free conjugate gradient algorithm. The final scheme can be regarded as a novel shock‐capturing, conservative, and structure preserving semi‐implicit scheme for VRMHD. Several numerical tests are presented to show the main features of our novel divergence‐free semi‐implicit FV/FD solver: linear‐stability in the sense of Lyapunov is verified at a prescribed constant equilibrium solution; a second‐order of convergence is obtained for a smooth time‐dependent solution; shock‐capturing capabilities are proven against a standard set of stringent MHD shock‐problems; accuracy and robustness are verified against a non‐trivial set of two‐ and three‐dimensional MHD problems.

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r = \sqrt{x^{2} + y^{2} + z^{2}}

. The computational domain is a three‐dimensional periodic box

(x, y, z) \in {[- 0.55, 0.55]}^{3}

that is discretized with a mesh resolution of

Δ x = Δ y = Δ z = 1 / 150

.…”

Section: Numerical Validationmentioning

confidence: 99%

“…Here, the viscous and resistive Orszag‐Tang vortex system is set up in three‐space dimensions, following References 90, and 89 for ideal MHD. The plasma parameters are chosen to be

γ = \frac{5}{3}

μ = 1 0^{- 6}

η = 1 0^{- 3}

c_{v} = 1

and a Prandtl number of

P r = 0.72

.…”

Section: Numerical Validationmentioning

confidence: 99%

A novel structure preserving semi‐implicit finite volume method for viscous and resistive magnetohydrodynamics

Fambri

2021

Numerical Methods in Fluids

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show abstract

“…3D MHD blast wave. The three-dimensional blast wave problem can be built as the direct extension of what presented in the previous paragraph, see also [76], after re-defining the three-dimensional At the top, the two-dimensional physical domain, together with the graphical representation of the interpolating lines are shown. Then, the numerical solution along the one-dimensional cut-lines are plotted next to a reference solution for matter-density (top-left), pressure (top-right), absolute value of the velocity (bottom-left) and magnetic pressure (bottom-right).…”

Section: Three Dimensional Testsmentioning

confidence: 99%

A novel structure preserving semi-implicit finite volume method for viscous and resistive magnetohydrodynamics

Fambri

2020

Preprint

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In this work we introduce a novel semi-implicit structure-preserving finite-volume/finite-difference scheme for the viscous and resistive equations of magneto-hydrodynamics (MHD) based on an appropriate 3-split of the governing PDE system, which is decomposed into a first convective subsystem, a second subsystem involving the coupling of the velocity field with the magnetic field and a third subsystem involving the pressure-velocity coupling. The nonlinear convective terms are discretized explicitly, while the remaining two subsystems accounting for the Alfvén waves and the magneto-acoustic waves are treated implicitly. Thanks to this, the final algorithm is at least formally constrained only by a mild Courant-Friedrich-Levy (CFL) stability condition depending on the velocity field of the pure hydrodynamic convection. To preserve the divergence-free constraint of the magnetic field exactly at the discrete level, a proper set of overlapping dual (staggered) meshes is employed. In this numerical formulation, the resulting linear algebraic systems are shown to be symmetric and therefore can be very efficiently solved by means of a standard matrix-free conjugate gradient algorithm. One of the peculiarities of the presented algorithm is that the magnetic field is defined on the edges of the main grid, while the electric field is on the faces. The final scheme can be regarded as a novel shock-capturing, conservative and structure preserving semi-implicit scheme for the nonlinear viscous and resistive MHD equations. Several numerical tests are presented to show the main features of our novel divergence-free semi-implicit FD/FV solver: linear-stability in the sense of Lyapunov is verified at a prescribed constant equilibrium solution; a second-order of convergence is obtained for a smooth time-dependent solution of the original PDE system; shockcapturing capabilities are proven against a standard set of stringent MHD shock-problems; accuracy and robustness are verified against a non-trivial set of two-and three-dimensional MHD problems.

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“…Рассматривалось течение азота при температуре нормальных условий. В [16,17] выполнено численное моделирование турбулентного газодинамического течения в присутствии электромагнитного поля для задачи о вихре Орзага-Танга. В процессе эволюции вихря наблюдалось формирование трехмерных ударных волн.…”

Section: Introductionunclassified

On the capabilities of the quasi-gasdynamic model for the numerical simulation of supersonic turbulent flows of interstellar gas

Елизарова

Shirokov²,

Попов

2017

KIAM Prepr.

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Smoothed MHD equations for numerical simulations of ideal quasi-neutral gas dynamic flows

Cited by 11 publications

References 38 publications

A novel structure preserving semi‐implicit finite volume method for viscous and resistive magnetohydrodynamics

A novel structure preserving semi‐implicit finite volume method for viscous and resistive magnetohydrodynamics

A novel structure preserving semi-implicit finite volume method for viscous and resistive magnetohydrodynamics

On the capabilities of the quasi-gasdynamic model for the numerical simulation of supersonic turbulent flows of interstellar gas

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