A numerical method for self-similar solutions of the ideal magnetohydrodynamics

Fang Chen, Ravi Samtaney

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We present a numerical method to obtain self-similar solutions of the ideal magnetohydrodynamics (MHD) equations. Under a self-similar transformation, the initial value problem (IVP) is converted into a boundary value prob1 lem (BVP) by eliminating time and transforming the system to self-similar coordinates (ξ ≡ x/t, η ≡ y/t). The ideal MHD system of equations is augmented by a generalized Lagrange multiplier (GLM) to maintain the solenoidal condition on the magnetic field. The self-similar solution to the BVP is solved using an iterative method, and implemented using the p4est adaptive mesh refinement (AMR) framework. Existing Riemann solvers (e.g., Roe, HLLD etc.) can be modified in a relatively straightforward manner and used in the present method. Numerical tests numerical tests illustrate that the present self-similar solution to the BVP exhibits sharper discontinuities than the corresponding one solved by the IVP. We compare and contrast the IVP and BVP solutions in several one dimensional shock-tube test problem and two dimensional test cases include shock wave refraction at a contact discontinuity, reflection at a solid wall, and shock wave diffraction over a right angle corner.
Original languageEnglish (US)
Pages (from-to)110690
JournalJournal of Computational Physics
StatePublished - Sep 10 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-09-13
Acknowledged KAUST grant number(s): BAS/1/1349-01-01
Acknowledgements: The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST) under grant no. BAS/1/1349-01-01.

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications


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