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A Finite Volume Method for the 3D Lagrangian Ideal Compressible Magnetohydrodynamics

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Abstract

We propose a cell-centered Lagrangian scheme for solving the three dimensional ideal magnetohydrodynamics (MHD) equations on unstructured meshes. The physical conservation laws are compatibly discretized on the unstructured meshes to satisfy the geometric conservation law (GCL). By introducing a generalized Lagrange multiplier, the magnetic divergence constraint is coupled with the conservation laws hence the magnetic divergence errors can dissipate and transport to the domain boundaries. Invoking the Galilean invariance, magnetic flux conservation and the thermodynamic consistency, the nodal approximate Riemann solver is derived and the corresponding first order finite volume scheme is then constructed. The piecewise linear spatial reconstruction and two step predictor corrector time integration are then adopted to increase the accuracy of the scheme. Various numerical tests are presented to assert the robustness and accuracy of our scheme.

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Acknowledgements

The authors would thank the anonymous reviewers for their thoughtful comments and useful suggestions. The authors are partially supported by NSFC (NO. 11171154, 11671050, 11771055, 11771053) and the Foundation of CAEP(CX20210044).

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Authors and Affiliations

  1. Graduate School of China Academy of Engineering Physics, Beijing, 10088, China

    Xiao Xu

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 10088, China

    Xiao Xu & Guoxi Ni

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  1. Xiao Xu
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  2. Guoxi Ni
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Correspondence to Guoxi Ni.

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Xu, X., Ni, G. A Finite Volume Method for the 3D Lagrangian Ideal Compressible Magnetohydrodynamics. J Sci Comput 91, 73 (2022). https://doi.org/10.1007/s10915-022-01851-6

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  • DOI: https://doi.org/10.1007/s10915-022-01851-6

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