Boundary element formulation using relative quantity for viscous flow

Abstract

The regularizing using relative quantity is applied to the problems of incompressible viscous flow in two dimensions. The regularized boundary integral equation for flow rate is obtained by superposing a particular solution of uniform flow rate upon the usual equation in the case of both finite and infinite region. The relative quantity is also introduced into the internal integral equations for flow rate and pressure. Since the integral equations for flow rate from inside to boundary become continuous, the integral equation for surface pressure is obtained, which has hitherto been absent in usual formulations. As a result, numerical results both of flow rate and pressure become very accurate all over the domain. Through two-dimensional examples of finite and infinite region, the new equations are verified to be correct.