A Particle Method without Remeshing

Abstract

We propose a simple tweak to a recently developed regularisation scheme for particle methods. This allows us to chose the particle spacing $h$ proportional to the regularisation length $\sigma$ and achieve optimal error bounds of the form $\mathcal{O}({\sigma }^n)$, $n\in \mathbb{N}$, without any need of 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.

References in corpus (2)

• Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations
• A Smooth Partition of Unity Finite Element Method for Vortex Particle Regularization