We present an innovative n umerical approach for setting highly accurate nonlocal boundary conditions at the external computational boundaries when calculating three-dimensional compressible viscous ows over nite bodies. The approach is based on application of the di erence potentials method by V . S . R y aben'kii and extends our previous technique developed for the two-dimensional case. The new boundary conditions methodology has been successfully combined with the NASA-developed code TLNS3D and used for the analysis of wing-shaped congurations in subsonic and transonic ow regimes. As demonstrated by the computational experiments, the improved external boundary conditions allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable speedup of convergence of the multigrid iterations.1 I n troduction Preliminaries. External ows over nite bodies or con gurations of bodies represent a wide class of important practical applications in uid dynamics. To treat this type of problems numerically, one typically truncates the original in nite domain. The resulting truncated problem is obviously subde nite unless supplemented by the proper closing procedure at the external computational boundary. The latter procedure is called the arti cial boundary conditions ABC's. In the ideal case, the ABC's would be speci ed so that the solution on the truncated domain coincides with the corresponding fragment of the original in nite-domain solution. The issue of ABC's is signi cant in CFD and in other areas of scienti c computing; theoretical estimates and computational experiments by di erent authors show that the proper treatment of external boundaries has a profound impact on the overall performance of numerical algorithms and interpretation of the results.Di erent ABC's methodologies have been studied extensively over the recent t w o decades. However, the construction of the ideal i.e., exact ABC's that would provide no error associated with the domain truncation and at the same time be computationally inexpensive, easy to implement, and geometrically universal, still remains a fairly remote possibility. Among the variety of approaches proposed to date only a few can be regarded as the commonly used tools in CFD. As a rule, these approaches are based on the essential model simpli cations e.g., locally one-dimensional treatment near the external boundary and, therefore, often lack accuracy in computations. This, in turn, necessitates choosing excessively large computational domains. On the other hand, these simple methods usually provide for local ABC's, and, therefore, for cheap, geometrically universal, and algorithmically simple numerical procedures, which are attractive for practical use.There are, of course, methods of another kind, which t ypically provide for highly accurate and robust numerical algorithms. These methods, however, are not used routinely because the corresponding ABC's in most cases appea...
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