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arXiv · 2411.13772

A Characteristic Mapping Method with Source Terms: Applications to Ideal Magnetohydrodynamics

Xi-Yuan Yin·Philipp Krah·Jean-Christophe Nave·Kai Schneider
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Abstract

This work introduces a generalized characteristic mapping method designed to handle non-linear advection with source terms. The semi-Lagrangian approach advances the flow map, incorporating the source term via the Duhamel integral. We derive a recursive formula for the time decomposition of the map and the source term integral, enhancing computational efficiency. Benchmark computations are presented for a test case with an exact solution and for two-dimensional ideal incompressible magnetohydrodynamics (MHD). Results demonstrate third-order accuracy in both space and time. The submap decomposition method achieves exceptionally high resolution, as illustrated by zooming into fine-scale current sheets. An error estimate is performed and suggests third order convergence in space and time.

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BibTeXRIS

Xi-Yuan Yin, Philipp Krah, Jean-Christophe Nave, Kai Schneider. 2024-11-21. A Characteristic Mapping Method with Source Terms: Applications to Ideal Magnetohydrodynamics. https://doi.org/10.1016/j.jcp.2026.114766

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