An open boundary condition for incompressible stratified flows

Orlanski's open boundary condition ( J. Comput. Phys. 21 (1976), 251) with a simple finite difference representation has been tested for laminar wakes in a nonstratified fluid and for internal wave problems in a linearly stratified flow. No artificial damping or filtering is applied to minimize high-frequency errors. Three test calculations, which are all linear flow problems, are carried out and compared with the exact solutions to demonstrate the accuracy of the open boundary condition. The performance of the open boundary condition is remarkably good. The test results also confirm that this type of boundary condition, which was originally designed by Orlanski primarily for equations which are hyperbolic in nature, also performs well for parabolic problems. Attention is needed, however, on implementing an open boundary condition for the pressure equation, especially when the flow dictates that the pressure field is strongly coupled with the velocity field.