On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation

This contribution discusses the construction of kernel-based adaptive particle methods for numerical flow simulation, where the finite volume particle method (FVPM) is used as a prototype. In the FVPM, scattered data approximation algorithms are required in the recovery step of the WENO reconstruction. We first show how kernel-based approximation schemes can be used in the recovery step of particle methods, where we give preference to the radial polyharmonic spline kernel. Then we discuss important aspects concerning the numerical stability and approximation behaviour of polyharmonic splines. Moreover, we propose customized coarsening and refinement rules for the adaptive resampling of the particles. Supporting numerical examples and comparisons with other radial kernels are provided.