Discrete Projections: A Step Towards Particle Methods on Bounded Domains without Remeshing

SIAM Journal on Scientific Computing, vol. 43, pp. A609–A635

Abstract

We propose a simple tweak to a recently developed regularization scheme for particle methods. This allows us to choose the particle spacing $h$ proportional to the regularization length $\sigma$ and achieve optimal error-bounds of the form $\mathcal{O}(\sigma^n)$, $n\in\mathbb{N}$, without any need for remeshing. We prove this result for the linear advection equation but also carry out high-order experiments on the full Navier--Stokes equations. In our experiments the particle methods proved to be highly accurate, long-term stable, and competitive with discontinuous Galerkin methods.

Authors 1

1. Matthias Kirchhart corresponding Aachen Center for Computational Engineering Science Mathematics Division

   RWTH Aachen University

   Affiliation as printed

   Center for Computational Engineering Science, Mathematics Division, RWTH Aachen University, Aachen, Germany