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Snapshot: multiphysics coupling talk at the 19th MHD Days in Potsdam

At this year's MHD Days our group member Simon Candelaresi presented his latest work on adaptive model selection in multiphysics coupling using Trixi.jl. There was a lively exchange of ideas with other researchers who use and develop methods of studying magnetohydrodynamic phenomena in laboratory plasma and astrophysics up to cosmic length scale. The MHD Days have been a? regular event since 1997.

Together with Arpit Babbar and Hendrik Ranocha, we have submitted our paper "Automatic differentiation for Lax-Wendroff-type discretizations".

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arXiv:2506.11719 reproduce me!

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Abstract

Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbolic conservation laws. In this work, we introduce automatic differentiation (AD) in the element-local time average flux computation step (the predictor step) of Lax-Wendroff methods. The application of AD is similar for methods of any order and does not need positivity corrections during the predictor step. This contrasts with the approximate Lax-Wendroff procedure, which requires different finite difference formulas for different orders of the method and positivity corrections in the predictor step for fluxes that can only be computed on admissible states. The method is Jacobian-free and problem-independent, allowing direct application to any physical flux function. Numerical experiments demonstrate the order and positivity preservation of the method. Additionally, performance comparisons indicate that the wall-clock time of automatic differentiation is always on par with the approximate Lax-Wendroff method.

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