A Meshfree Generalization of the Finite Volume Method
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The Finite Volume Particle Method (FVPM) is a meshfree generalization of the well known Finite Volume Method. It combines the advantages of Finite Volume Method with those of classical Particle Methods. Hence, it is quantity conserving, stable and efficiently covers changing domains due to its ALE-property. Finally, it is perfectly suited for the simulation of free-surface flows. We implemented a tree-based version of FVPM to simplify neighbor search, MPI parallelization and a satisfactory uniform and hence efficient particle distribution, i.e. we avoid artificial holes in the covering as well as large local neighborhoods due to particle crowding. This allows us to compute large fluid dynamic problems on changing domains in three dimensions efficiently in appropriate time. Furthermore, it enables future coupling with other meshfree methods. A natural candidate here is the Partition of Unity Method (PUM), since both methods are based on a partition of unity on their discretization cells and on the same underlying tree structure. This coupling will allow us to optimize the simulation of complex applications including fluid- and elastodynamic processes such as fluid-structure interaction or problems including phase changes of moving fluid as in additive manufacturing processes on micro-scale.