EXTERNAL BOUNDARY CONDITIONS FOR THREE-DIMENSIONAL PROBLEMS OF COMPUTATIONAL AERODYNAMICS

Abstract. We consider an unbounded steady-state °ow of viscous °uid over a three-dimensional nite body or conguration of bodies. For the purpose of solving this °ow numerically, we discretize the governing equations (Navier{Stokes) on a nite-dierence grid. Prior to the discretization, we obviously need to truncate the original unbounded domain by introducing an articial computational boundary at a nite distance from the body; otherwise, the number of discrete variables will not be nite. This articial boundary is typically the external boundary of the domain covered by the grid. The °ow problem (both continuous and discretized) formulated on the nite computational do-main is clearly subdenite unless supplemented by some articial boundary conditions (ABCs) at the external computational boundary. In this paper, we present an innovative approach to constructing highly accurate ABCs for three-dimensional °ow computations. The approach extends our previ-ous technique developed for the two-dimensional case; it employs the nite-dierence counterparts to Calderon’s pseudodierential boundary projections calculated in the framework of the dierence potentials method (DPM) of Ryaben’kii. The resulting ABCs appear spatially nonlocal but are particularly easy to implement along with the existing °ow solvers. The new boundary conditions have been successfully combined with the NASA-developed pro