A Particle Method without Remeshing
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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 σ and achieve optimal error bounds of the form O(σ^n), n∈N, without any need of remeshing. We prove this result for the linear advection equation but 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.
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