Discrete Singular Convolution–Finite Subdomain Method for the Solution of Incompressible Viscous Flows

Abstract

This paper proposes a discrete singular convolution-finite subdomain method (DSC–FSM) for the analysis of incompressible viscous flows in multiply connected complex geometries. The DSC algorithm has its foundation in the theory of distributions. A block-structured grid of fictitious overlapping interfaces is designed to decompose a complex computational geometry into a finite number of subdomains. In each subdomain, the governing Navier–Stokes equations are discretized by using the DSC algorithm in space and a third-order Runge–Kutta scheme in time. Information exchange between fictitious overlapping zones is realized by using the DSC interpolating algorithm. The Taylor problem, with decaying vortices, could be solved to machine precision, with an excellent comparison against the exact solution. The reliability of the proposed method is tested by simulating the flow in a lid-driven cavity. The utility of the DSC–FSM approach is further illustrated by two other benchmark problems, viz., the flow over a backward-facing step and the laminar flow past a square prism. The present results compare well with the numerical and experimental data available in the literature.