Workshop on Particle-based simulation methods 5-6 Nov 2024
We would like to invite you to the upcoming CAAPS Workshop on Particle-based numerical simulations, which will take place at the Centre for Advanced Analytics and Predictive Sciences of the 伟德国际_伟德国际1946$娱乐app游戏 of Augsburg on 5th and 6th November 2024. ? Abstract Particle-based simulations are a versatile tool for numerically investigating complex physical systems, including fluid dynamics, solid mechanics, and multi-physics problems. They are well-suited for a number of applications that are difficult to address using traditional grid-based methods, but present their own set of challenges in terms of accuracy, stability, and computational efficiency. In this workshop, researchers from various scientific disciplines come together to discuss recent advancements in particle-based simulations. In addition to exploring innovative modeling approaches and developments in numerical methods, the workshop places special emphasis on efficient algorithms and modern implementation techniques. The first day features presentations from experts in the field, while the second day hosts a hackathon, offering practitioners the chance to work on their own projects and collaborate with fellow participants. ? You can find further information
here. Registration is not mandatory but appreciated, as it helps us with organization and catering.
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.