Volume 3, Issue 4
Gas-Kinetic BGK Scheme for Three Dimensional Magnetohydrodynamics

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 387-404.

Published online: 2010-03

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• Abstract

The gas-kinetic theory based flux splitting method has been successfully proposed for solving one- and two-dimensional ideal magnetohydrodynamics by Xu et al. [J. Comput. Phys., 1999; 2000], respectively. This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations, where an adaptive parameter $\eta$ is used to control the numerical dissipation in the flux splitting method. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.

• Keywords

The kinetic BGK scheme, magnetohydrodynamics, divergence-free condition.

76M25, 76W05

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@Article{NMTMA-3-387, author = {}, title = {Gas-Kinetic BGK Scheme for Three Dimensional Magnetohydrodynamics}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {4}, pages = {387--404}, abstract = {

The gas-kinetic theory based flux splitting method has been successfully proposed for solving one- and two-dimensional ideal magnetohydrodynamics by Xu et al. [J. Comput. Phys., 1999; 2000], respectively. This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations, where an adaptive parameter $\eta$ is used to control the numerical dissipation in the flux splitting method. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.m9007}, url = {http://global-sci.org/intro/article_detail/nmtma/6005.html} }
TY - JOUR T1 - Gas-Kinetic BGK Scheme for Three Dimensional Magnetohydrodynamics JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 387 EP - 404 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.m9007 UR - https://global-sci.org/intro/article_detail/nmtma/6005.html KW - The kinetic BGK scheme, magnetohydrodynamics, divergence-free condition. AB -

The gas-kinetic theory based flux splitting method has been successfully proposed for solving one- and two-dimensional ideal magnetohydrodynamics by Xu et al. [J. Comput. Phys., 1999; 2000], respectively. This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations, where an adaptive parameter $\eta$ is used to control the numerical dissipation in the flux splitting method. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.

Huazhong Tang, Kun Xu & Chunpei Cai. (2020). Gas-Kinetic BGK Scheme for Three Dimensional Magnetohydrodynamics. Numerical Mathematics: Theory, Methods and Applications. 3 (4). 387-404. doi:10.4208/nmtma.2010.m9007
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