New paper: TrixiParticles.jl: Particle-based multiphysics simulation in Julia
TrixiParticles.jl is a Julia-based open-source package for particle-based multiphysics simulations and part of the
Trixi Framework. It handles complex geometries and specialized applications, such as computational fluid dynamics (CFD) and structural dynamics, by providing a versatile platform for particle-based methods. TrixiParticles.jl allows for the straightforward addition of new particle systems and their interactions, facilitating the setup of coupled multiphysics simulations such as fluid-structure interaction (FSI). Furthermore, simulations are set up directly with Julia code, simplifying the integration of custom functionalities and promoting rapid prototyping. ?
Together with Arpit Babbar and Hendrik Ranocha, we have submitted our paper "Automatic differentiation for Lax-Wendroff-type discretizations".
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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.