This paper presents the development of locally divergence-free (LDF) oscillation-eliminating discontinuous Galerkin (OEDG) schemes for the ideal magnetohydrodynamics (MHD) equations. The key highlights are:
The LDF OEDG schemes are designed to suppress spurious oscillations near strong discontinuities while maintaining the locally divergence-free property of the computed magnetic field. This is achieved by performing oscillation elimination (OE) steps for Legendre polynomials and LDF polynomials separately using the LDF DG method as the base scheme.
A positivity-preserving (PP) analysis of the LDF OEDG schemes is provided on Cartesian meshes. By employing the LDF OEDG scheme, PP limiter, HLL flux, and properly discretized Godunov-Powell source term, the PP property is proved via general convex decomposition techniques.
Numerical examples in one and two dimensions demonstrate the accuracy, effectiveness, and robustness of the proposed LDF OEDG schemes in handling ideal MHD problems with strong discontinuities.
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by Mengqing Liu... um arxiv.org 04-26-2024
https://arxiv.org/pdf/2404.16794.pdfTiefere Fragen