Meshless generalized finite difference method with a domain-selection method for solving degenerate boundary problems

Abstract

This paper is dedicated to presenting a combined Generalized Finite Difference Method (GFDM) and Domain-Selection Method (DSM) approach for solving degenerate boundary problems which are usually encountered in engineering simulations. Compared with traditional Domain-Decomposition Method (DDM), the most critical advantage of the present GFDM-DSM is that it is entirely free from matching continuous boundary conditions for different parts of the fluid domain of interest, which is sometimes hard to perform for specific situations. Instead, the only prerequisite of the present GFDM-DSM is to identify which sub-domain each computational node belongs to, and then a linear algebraic system can be assembled according to the pattern of domain-selection. Four benchmarks are performed to validate the convergence and accuracy of the present GFDM-DSM. It is shown that the present GFDM-DSM holds satisfactory accuracy for solving degenerate boundary problems. In particular, the present DSM is a flexible strategy since it can be also combined with other localized domain-type meshless methods in practical applications.