Stabilization of RBF-generated finite difference methods for convective PDEs

Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs because of their ability to achieve spectral accuracy also with unstructured node layouts. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD) methods can offer significant savings in computer resources (time and memory). This study presents a new filter mechanism, allowing such gains to be realized also for purely convective PDEs that do not naturally feature any stabilizing dissipation.