Explicit formulations for evaluation of velocity gradients using boundary-domain integral equations in 2D and 3D viscous flows
In this paper, explicit boundary-domain integral equations for evaluating velocity gradients are derived from the basic velocity integral equations. A free term is produced in the new strongly singular integral equation, which is not included in recent formulations using the complex variable differentiation method (CVDM) to compute velocity gradients (Int. J. Numer Meth. Fluids 2004; 45:463-484; Int. J. Numer. Meth. Fluids 200i; 47:19-43). The strongly singular domain integrals involved in the new integral equations are accurately evaluated using the radial integration method (RIM). Considerable computational time for evaluating integrals of velocity gradients can be saved by using present formulation than using CVDM. The formulation derived in this paper together with those presented in reference (Int. J. Numer Meth. Fluids 2004; 45:463-484) for 2D and in (Int. J. Numer. Meth. Fluids 2005; 47:19-43) for 3D problems constitutes a complete boundary-domain integral equation system for solving full Navier-Stokes equations using primitive variables. Three numerical examples for steady incompressible viscous flow are given to validate the derived formulations. Copyright (C) 2007 John Wiley & Sons, Ltd.
viscous flow complex variable differentiation method (cvdm) navier-stokes equations boundary element method (bem) fundamental solution