Snapshot: SPH simulation of the liquefaction of the Julia logo
2D single-phase simulation of the liquefaction of the Julia logo with TrixiParticles.jl. The letters are simulated as a fluid with the Weakly Compressible SPH (WCSPH) method and the dots are simulated as an elastic solid with the Total Lagrangian SPH (TLSPH) method for structure mechanics. This snapshot was created by
Niklas Neher. Cross-posted with
https://www.mi.uni-koeln.de/NumSim/2024/07/04/snapshot-multiphysics-sph-simulation-of-the-liquefaction-of-the-julia-logo/.
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.