The Hermite radial basis function control volume method for multi-zones problems; A non-overlapping domain decomposition algorithm

Abstract

In this paper a non-overlapping non-iterative multi-domain formulation for the control volume Hermite radial basis functions (CV-HRBF) method is proposed, where the local Hermitian RBF meshless collocation method is used to satisfy a physical matching condition at the sub-domain boundaries. In addition, the robustness of the Hermite interpolation is exploited even further to apply multiple flux continuities for those cases where more than two sub-domains converge in the same point. The algorithm is first validated in one-dimensional advection diffusion problems for which an analytical solution is known. Its accuracy is compared with a classic CV approach and a local radial basis function collocation method (LRBFCM). More general applications in two and three-dimensional domains are then considered. A heat transfer problem in strongly heterogeneous materials, and a groundwater flow problem in presence of geological layers characterised by different hydraulic conductivity, are taken as engineering applications to test the capabilities of the CV-HRBF method to handle multi-zone problems. Finally, the transport of a single species is simulated in a one-dimensional channel consisting of two adjacent zones that feature different Peclet numbers.