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This paper proposes and analyzes a robust and efficient second-order positivity-preserving constrained transport (PPCT) scheme for ideal magnetohydrodynamics (MHD) on non-staggered Cartesian meshes. The PPCT scheme ensures two critical physical constraints: a globally discrete divergence-free (DDF) condition on the magnetic field and the positivity of density and pressure. The method is inspired by a novel splitting technique from [T.A. Dao, M. Nazarov and I. Tomas, J. Comput. Phys., 508:113009, 2024], which divides the MHD system into an Euler subsystem with steady magnetic fields and a magnetic subsystem with steady density and internal energy. To achieve these structure-preserving properties, the PPCT scheme combines a positivity-preserving (PP) finite volume method for the Euler subsystem with a finite difference constrained transport (CT) method for the magnetic subsystem via Strang splitting. The finite volume method employs a new PP limiter that retains second-order accuracy and enforces the positivity of density and pressure, with rigorous proof provided using the geometric quasilinearization (GQL) approach [K. Wu and C.-W. Shu, SIAM Review, 65:1031-1073, 2023]. For the mag

Author

Pang, Dongwen; Wu, Kailiang

Published

2024

Language

EN