High-Order Fully Coupled Scheme Based on Compact Integrated RBF Approximation for Viscous Flows in Regular and Irregular Domains

In this study, we present a numerical discretisation scheme, based on a direct fully coupled approach and compact integrated radial basis function (CIRBF) approximations, to simulate viscous flows in regular/irregular domains. The governing equations are taken in the primitive form where the velocity and pressure fields are solved in a direct fully coupled approach. Compact local approximations, based on integrated radial basis functions, over 3-node stencils are introduced into the direct fully coupled approach to represent the field variables. The present scheme is verified through the solutions of several problems including Poisson equations, Taylor-Green vortices and lid driven cavity flows, defined on domains of different shapes. The numerical results obtained by the present scheme are highly accurate and in good agreement with those reported in earlier studies of the same problems.