From the summary: While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABCs) at the newly formed external boundary. The issue of setting the ABCs appears most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems represent a wide class of important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms and interpretation of the results.
In this paper we first present an extensive survey and provide a comparative assessment of different existing methods for constructing the ABCs. Then, we describe a new ABCs technique proposed in our recent work and review the corresponding results. This new technique enables one to construct the ABCs that largely combine the advantages relevant to the two aforementioned classes of existing methods.