A new integrated-rbf-based domain-embedding scheme for solving fluid-flow problems

Abstract

[Abstract]: This paper presents a new domain embedding numerical scheme for the simulation of flows of a Newtonian fluid in multiply-connected domains. The governing equations are taken from the stream function-vorticity formulation. The problem domain is converted into a simply-connected domain that is then discretised using a Cartesian grid. Radial-basis-function networks, which are constructed through integration rather than the usual differentiation, are employed on grid lines to approximate the field variables. Each field variable is assumed to vary over interior holes according to appropriate polynomials that satisfy the boundary conditions. Point collocation is applied to discretise the governing equations. Several linear and nonlinear problems, including natural convection in the annulus between square and circular cylinders are simulated to verify the proposed technique.