A Fully Coupled Scheme for Viscous Flows in Regular and Irregular Domains Using Compact Integrated RBF Approximation

Abstract

In this study, we present a numerical discretisation scheme, based on a fully coupled approach and compact local integrated radial basis function (CIRBF) approximations, to solve the Navier-Stokes equation in rectangular/non-rectangular domains. The velocity and pressure fields are simulated in a fully coupled manner [1] with Cartesian grids. The field variables are locally approximated in each direction by using CIRBF approximations defined over 3-node stencils, where nodal values of the first-and second-order derivatives of the field variables are also included [2, 3]. The present scheme, whose system matrix is sparse, is verified through the solutions of several test problems including Taylor-Green vortices. Highly accurate solutions are obtained.