To the boundary and back - A numerical study

The key parameters are identified upon which energy absorption at artificial boundaries depends. A thorough numerical study is presented, of typical reflections from open computational boundaries, for problems governed by hyperbolic systems of equations. The emphasis is on systems where the combination of all boundary procedures determine the quality of boundary treatment. Dissipative numerical models are studied which have so far not been analyzed to the same extent as nondissipative models and a Lax-Wendroff-type scheme is employed as a prototype. While it is widely accepted that dissipative models tend to give fewer problems than nondissipative ones, a variety of cases demonstrate that substantial reflections occur even in 1D and quasi-1D set-ups, where theory predicts best results. This can partly be explained by the vanishing of dissipation in the far field. Group velocity analysis, justifiable on the grounds of weak dissipation, predicts a pathological behavior which is confirmed by numerical experiments. Strong focusing of asymptotic errors generated at the artificial boundary are demonstrated, and internal reflections due to slowly expanding grids are shown for nonlinear systems. The need for high-frequency boundary conditions naturally arises and combined low-high-frequency boundary recipes are adapted to systems and tested. Partial cures are also discussed, mainly in terms of pointing out their theoretically limited potential.