Time dependent boundary conditions for hyperbolic systems

Abstract

Time dependent numerical models for hyperbolic systems, such as the fluid dynamics equations, require time dependent boundary conditions when the systems are solved in a finite domain. The “correct” boundary condition depends on the external solution, but for many problems the external solution is not known. In such cases nonreflecting boundary conditions often produce solutions with the desired behavior. This paper extends the concept of nonreflecting boundary conditions to the multidimensional case in non-rectangular coordinate systems. Results are given for several fluid dynamics test problems: the traveling shock wave, shock tube, spherical explosion, and homologous expansion problems in one dimension, and a traveling shock wave moving at a 45° angle with respect to the x axis in two dimensions.