Numerical Boundary Conditions for Viscous Flow Problems

A method for treating certain troublesome boundary conditions in the numerical solution of time-dependent incompressible viscous flow problems is presented. This method is developed on the basis of an integral representation for the velocity vector which contains the entire kinematics of the problem, including the boundary conditions of concern. It is shown that for the exterior flow problem the freestream condition is satisfied at infinity exactly, and the need to treat a farfield condition is removed by the use of the integral representation. The distribution of a nonvelocity variable on the solid boundary, i.e., the extraneous boundary condition needed for both the exterior and the interior flows, are shown to be governed by the kinematics of the problem. The method is shown to accurately follow the local generation of vorticity on the solid boundary computationally.