High-Order Upwind Methods Based on C~2-Continuous Two-Node Integrated-RBF Elements for Viscous Flows

摘要

In this paper, 2-node integrated radial basis function elements (IRBFEs) [CMES, vol.72, no.4, pp.299-334, 2011] are further developed for the simulation of incompressible viscous flows in two dimensions. Emphasis is placed on (i) the incorporation of C~2-continuous 2-node IRBFEs into the subregion and point collocation frameworks for the discretisation of the stream function-vorticity formulation on Cartesian grids; and (ii) the development of high order upwind schemes based on 2-node IRBFEs for the case of convection-dominant flows. High levels of accuracy and efficiency of the present methods are demonstrated by solutions of several benchmark problems defined on rectangular and non-rectangular domains.