Large Scale, Multiresolution Flow Simulations Using Remeshed Particle Methods

Abstract

Particle methods are a robust and versatile computational tool for the simulation of continuous and discrete physical systems ranging from Fluid Mechanics to Biology and Social Sciences. In advection dominated problems particle methods can be considered as the method of choice due to their inherent robustness, stability and Lagrangian adaptivity. At the same time however, smooth particle methods encounter major difficulties in simulating the equations they set out to discretize when their computational elements fail to overlap, a condition necessary for their convergence [2]. A number of ad-hoc parameters and artificial dissipation techniques are often introduced in techniques such as Smoothed Particle Hydrodynamics (SPH) [15, 19] in order to remedy these difficulties.

In the present paper we demonstrate that the convergence of smooth particle methods can be ensured by a periodic remeshing of the particles using high-order interpolation kernels. This procedure retains the Lagrangian character and stability of particle methods and enables the control of their accuracy [5, 9, 16, 17] while introducing numerical dissipation at levels well below those introduced by temporal discretizations.

In addition, remeshing enables two major improvements over grid-free particle methods: First by exploiting the regularity of the remeshed particles, it reduces by at least an order of magnitude their computational cost [6, 10] and facilitates their massively parallel implementation. Second, remeshing enables the development of consistent multiresolution techniques such as wavelet-particle methods [4]. This approach has been implemented efficiently in massively parallel computer architectures allowing for unprecedented vortex dynamics simulations using billions of particles.