Accurate and Robust Pressure Weight Advection Upstream Splitting Method for Magnetohydrodynamics Equations

Han, Sang-Hoon; Lee, Jeong-Il; Kim, Kyu Hong

doi:10.2514/1.39375

Cited by 33 publications

(38 citation statements)

References 34 publications

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“…Since the Orszag-Tang MHD turbulence problem [60] has many significant characteristics of MHD turbulence, such as interactions of multiple shock waves generated as the vortex evolves, it is considered as one of the standard models to validate a MHD numerical method [61,4,62,19,37]. The initial conditions are given by qðx; y; 0Þ ¼ c 2 ; uðx; y; 0Þ ¼ À sinðyÞ; vðx; y; 0Þ ¼ sinðxÞ; pðx; y; 0Þ ¼ c; B x ðx; y; 0Þ ¼ À sinðyÞ; B y ðx; y; 0Þ ¼ sinð2xÞ; where c ¼ 5=3.…”

Section: Orszag-tang Mhd Turbulence Problemmentioning

confidence: 99%

“…However, as discussed in [37], the low diffusion scheme combined with high-order reconstruction is more prone to yield numerical oscillations in a shock wave. Agarwal et al [38] applied the original AUSM method with first-order spatial accuracy to one-dimensional MHD cases.…”

Section: Introductionmentioning

confidence: 99%

“…Agarwal et al [38] applied the original AUSM method with first-order spatial accuracy to one-dimensional MHD cases. Han et al [37] developed a AUSMPW+/M-AUSMPW + schemes combined with the MLP (multidimensional limiting process) interpolation method to achieve the higher order accuracy for MHD equations.…”

Section: Introductionmentioning

confidence: 99%

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E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

Shen

Zha

Huerta

2012

Journal of Computational Physics

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a b s t r a c tAn E-CUSP (energy-convective upwind and split pressure) scheme is developed to solve the equations of magnetohydrodynamics. Fifth order WENO reconstructions are employed to calculate the fluxes in order to achieve high order spacial accuracy. A characteristic speed of sound by averaging the fast wave speed and the acoustic speed of sound is suggested to evaluate the Mach number, which will yield robust and accurate solutions. The numerical experiments have demonstrated the accuracy and the capability of the new scheme to capture complex interactions of multiple shocks and vortices.

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Section: Orszag-tang Mhd Turbulence Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

Shen

Zha

Huerta

2012

Journal of Computational Physics

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“…However, as discussed in [33], the low diffusion scheme combined with high-order reconstruction is much more probable to yield numerical oscillations in a shock wave. Agarwal et al [34] applied the original AUSM method with first-order spatial accuracy to one-dimensional MHD cases.…”

Section: Introductionmentioning

confidence: 99%

“…Agarwal et al [34] applied the original AUSM method with first-order spatial accuracy to one-dimensional MHD cases. Han et al [33] developed a AUSMPW+/M-AUSMPW+ schemes combined with the MLP interpolation method to achieve the higher order accuracy for MHD equations.…”

Section: Introductionmentioning

confidence: 99%

A Constrained-Transport E-CUSP scheme for Ideal Magnetohydrodynamic Equations

Shen

Zha

Huerta

2011

42nd AIAA Plasmadynamics and Lasers Conference

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A pressure‐based method with AUSM‐type fluxes for MHD flows at arbitrary Mach numbers

Xisto

Páscoa

Oliveira

2013

Numerical Methods in Fluids

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SUMMARY In this paper, we propose an extension of a PISO method, previously developed to solve the Euler equations, and which is here extended to the ideal magnetohydrodynamic (MHD) equations. By following a pressure‐based approach, we make use of the flexibility given by pressure equation for calculating flows at arbitrary Mach numbers. To handle MHD discontinuities, we have adapted the MHD‐Advection Upstream Splitting Method for our pressure‐based formulation. With the purpose of validation, four sets of test cases are presented and discussed. We start with the circularly polarized Alfvén waves that serves as a smooth flow validation. The second case is the 1‐D Riemann problem that is calculated using both 1‐D and 2‐D formulation of the MHD equations. The third and fourth problems are the Orszag–Tang vortex and the supersonic low‐ β cylinder allowing validation of the method in complex 2‐D MHD shock interaction. Copyright © 2013 John Wiley & Sons, Ltd.

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Accurate and Robust Pressure Weight Advection Upstream Splitting Method for Magnetohydrodynamics Equations

Cited by 33 publications

References 34 publications

E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

A Constrained-Transport E-CUSP scheme for Ideal Magnetohydrodynamic Equations

A pressure‐based method with AUSM‐type fluxes for MHD flows at arbitrary Mach numbers

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