Tree-based meshfree generalization of the Finite Volume Method

The Finite Volume Particle Method (FVPM) is a meshfree generalization of the Finite Volume Method (FVM). It can handle a wide range of computational fluid dynamic problems including free surfaces, moving domains and shock fronts. Combining the particle method advantages with those of FVM, FVPM is conservative, stable and non-oscillating near shock fronts. Although this method is very promising, its typical realizations are computationally overly expensive and not trivial to parallelize. This paper aims to overcome this issue and make FVPM practically applicable to large high dimensional industrial problems. To this end, we significantly lower the computational costs and enable efficient parallelization by introducing an underlying tree structure and adaptive, dynamic load balancing. The underlying tree not only allows efficient particle memory handling but also improves particle movement efficiency, which substantially reduces the runtime. Standard particle method problems of artificial holes and particle crowding can entirely be avoided. This parallel tree-based approach hence highly expands the scope of possible FVPM applications. We verify this approach in numerical benchmark testcases, show it stability, and present its performant scaling behavior in two and three dimensional scenarios.