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

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 O (sigma(n)), n is an element of 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.