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High-Performance Scientific Computing

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Snapshot: Adaptive multiphysics coupling in Trixi.jl

Simple physical systems can be simulated using a single model. For instance, for gas dynamics we might choose to solve the Navier-Stokes equations. More complex systems require multiple descriptions. A heated material embedded in a gas flow could be described using the heat induction equations for the material and the Navier-Stokes for the gas. A magnetic reconnection event could be described using a kinetic description for the reconnection region and the magnetohydrodynamic (MHD) equations for the surrounding medium.

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Such multiphysics systems need to couple their constituents in a physically meaningful way. Here, we do this by coupling through the interface boundary where we transform variables between the systems using converter functions. This makes coupling very flexible so that even models that do not share variables, but share some of the physics, can be coupled.

To make the simulations more dynamic we also implemented adaptive model selection (AMS). By freely choosing criteria we can change the domains in which each model is being used. This allows us do adapt to the dynamics of the system.



For more information see: https://www.slideshare.net/slideshow/adaptively-coupled-multiphysics-simulations-with-trixi-jl/27043763
Adaptive model selection in a coupled MHD-Euler multiphysics simulation.

By coupling the interface boundary between Euler systems and one MHD system (center) we can simulate this multiphysics system while saving computational time. We define criteria for the adaptive model selection, so that the more complex model (MHD) is being simulated where it is needed. This has been implemented in the Trixi.jl code.

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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