Efficient Parallel Implementation of the Finite Volume Particle Method
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The Finite Volume Particle Method (FVPM) is a meshfree particle generalization of the well known Finite Volume Method. It combines the advantages of the Finite Volume Method with those of classical Particle Methods. Hence, it is quantity conserving, stable, and efficiently covers changing domains due to its Arbitrary-Lagrangian-Eulerian-property (ALE-property). Altogether, it is perfectly suited for simulating conservative free-surface flows. \\ However, as a particle method, it includes many computationally involved subroutines such as particle movement, changing neighborhoods, and the computation of particle interaction. Note that, due to the time dependency of fluid problems, those routines need to be done in every timestep. \\ To make these parts more efficient, we implement a tree-based version of FVPM -- meaning we associate particles with an octree covering the domain and use these tree cells for our computations exploiting the ALE-property of FVPM. This not only simplifies neighbor search and MPI parallelization, it also leads to a satisfactory uniform and hence efficient particle distribution, i.e. we avoid artificial holes in the covering as well particle crowding. This is to our knowledge the first MPI-parallelized implementation of FVPM. \\ The cell association process allows further optimization in timesteps, where not much particle movement takes place. \\ Another bottleneck is that various variables are defined by integrals. Therefore, the computation need numerical integration techniques, which are expensive and not exact. We use cubic particles and simple Partition of Unity functions to optimize this part of the computations as well. This enables the computation of integrals via analytic formulas and therefore avoid errors and efficiency-issues of numerical integration completely.\\ Altogether, we adapt the classical implementation of FVPM in various aspects to get a not only conservative but also efficient particle method applicable to large three-dimensional problems and engineering applications.