Abstract
In the numerical approximation of hyperbolic equations, outflow boundaries are in general not transparent, and they create spurious reflection. A useful measure of this is given by the energy (or usual sum of squares) of the reflected solution in response to an arbitrary solution, which originates from within the computing domain. We prove, in that respect, a somewhat unexpected property: Namely that for those full discretization which are obtained by applying to a space- discretization of the problem an energy conservative discrete time-marching method, the energy reflected at the boundary is independent of which time-marching method is used, of the value Af, and is strictly equal to the reflected energy in the semi-discrete case. This is also verified by numerical experiments. Optimal boundary equations may be defined in the semi-discrete case of those which maximize the rate of convergence to zero of the reflected energy when. H -->O . A corollary of the preceding result is that those boundary equations remain optimal, in the same sense, when used in an energy conservative full.