Geodesic
Non-local artificial boundary conditions for three-dimensional stationary flow problems
Matematičeskoe modelirovanie, Tome 10 (1998) no. 9, pp. 64-86.

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The problem of generating artificial boundary conditions on the external boundary of a computational domain for stationary aerodynamic transonic flow problems is considered. The analysis is made under assumption that outside a computational domain the flow is described by the Euler equations linearized about the free-stream subsonic uniform background. In order to find the desired conditions that are non-local and exact with respect to the considered model, the potential theory is used. The operator of boundary conditions requires only the evaluation of two surface integrals throughout an artificial boundary. We discuss the numerical implementation of proposed conditions in frames of relaxation methods for solving flow problems and estimate the necessary computational costs. Numerical results on testing of obtained computational formulae are given. 
@article{MM_1998_10_9_a5,
     author = {I. L. Sofronov},
     title = {Non-local artificial boundary conditions for three-dimensional stationary flow problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {64--86},
     publisher = {mathdoc},
     volume = {10},
     number = {9},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1998_10_9_a5/}
}
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I. L. Sofronov. Non-local artificial boundary conditions for three-dimensional stationary flow problems. Matematičeskoe modelirovanie, Tome 10 (1998) no. 9, pp. 64-86. http://geodesic.mathdoc.fr/item/MM_1998_10_9_a5/