English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce a novel structure-preserving method in order to approximate thecompressible ideal Magnetohydrodynamics (MHD) equations. This techniqueaddresses the MHD equations using a non-divergence formulation, where thecontributions of the magnetic field to the momentum and total mechanical energyare treated as source terms. Our approach uses the Marchuk-Strang splittingtechnique and involves three distinct components: a compressible Euler solver,a source-system solver, and an update procedure for the total mechanicalenergy. The scheme allows for significant freedom on the choice of Euler'sequation solver, while the magnetic field is discretized using acurl-conforming finite element space, yielding exact preservation of theinvolution constraints. We prove that the method preserves invariant domainproperties, including positivity of density, positivity of internal energy, andthe minimum principle of the specific entropy. If the scheme used to solveEuler's equation conserves total energy, then the resulting MHD scheme can beproven to preserve total energy. Similarly, if the scheme used to solve Euler'sequation is entropy-stable, then the resulting MHD scheme is entropy stable aswell. In our approach, the CFL condition does not depend on magnetosonicwave-speeds, but only on the usual maximum wave speed from Euler's system. Tovalidate the effectiveness of our method, we solve a variety of ideal MHDproblems, showing that the method is capable of delivering high-order accuracyin space for smooth problems, while also offering unconditional robustness inthe shock hydrodynamics regime as well.

Structure preserving numerical methods for the ideal compressible MHD system