Distribution of Artificial Selective Damping

Inclusion of artificial selective damping in a computation code is absolutely necessary if a central difference scheme is used. Central difference schemes have no intrinsic damping. Without artificial selective damping, such a computation would fail either because the solution is heavily polluted by spurious waves or through a blowup. In a typical numerical simulation, artificial selective damping has two roles to play. First and foremost, it eliminates spurious waves, especially grid-to-grid oscillations as they propagate across the computation domain. For this purpose, a standard practice is to add a general background damping throughout the entire computation domain. The mesh Reynolds number should be chosen so that any grid-to-grid oscillations are damped by several orders of magnitude when propagating from one side to the other side of a subdomain. The second purpose of imposing artificial selective damping
is to suppress the generation of spurious waves. Spurious waves are produced at surfaces of discontinuities. Thus, at solid surfaces, fluid interfaces, or mesh-size – change interfaces, extra artificial selective damping should be imposed. When a simulation contains solid surfaces with sharp edges and corners, one must recognize that these are sites for the generation of strong grid-to-grid oscillations. Grid-to – grid oscillations are one of the main causes of numerical instability. To suppress the generation of grid-to-grid oscillations, an effective method is to add additional artificial selective damping at and near sharp edges and corners.