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The scheme treats all terms associated with the acoustic pressure implicitly while keeping the remaining terms part of the explicit sub-system. This semi-implicit approach makes the method particularly well suited for problems in the low Mach regime. We combine the semi-implicit scheme with the deviation well-balancing technique and prove that it maintains equilibrium solutions for the magnetohydrostatic case up to rounding errors. In order to preserve the divergence-free property of the magnetic field enforced by the solenoidal constraint, we incorporate a constrained transport method in the semi-implicit framework. Second order of accuracy is achieved by means of a standard spatial reconstruction technique with total variation diminishing property, and by an asymptotic preserving time stepping algorithm built upon the implicit-explicit Runge\u2013Kutta time integrators. Numerical tests in the low Mach regime and near magnetohydrostatic equilibria support the low Mach and well-balanced properties of the numerical method.<\/jats:p>","DOI":"10.1007\/s10915-023-02422-z","type":"journal-article","created":{"date-parts":[[2024,1,3]],"date-time":"2024-01-03T06:02:06Z","timestamp":1704261726000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Well-Balanced Semi-implicit IMEX Finite Volume Scheme for Ideal Magnetohydrodynamics at All Mach Numbers"],"prefix":"10.1007","volume":"98","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4746-178X","authenticated-orcid":false,"given":"Claudius","family":"Birke","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Walter","family":"Boscheri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Klingenberg","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,1,3]]},"reference":[{"key":"2422_CR1","doi-asserted-by":"publisher","first-page":"970","DOI":"10.1137\/S1064827596304824","volume":"21","author":"T Amari","year":"1999","unstructured":"Amari, T., Luciani, J.F., Joly, P.: Preconditioned semi-implicit method for magnetohydrodynamics equations. 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