Artificial Selective Damping
As discussed before, artificial selective damping is incorporated into the DRP computational algorithm for two purposes. First, it is used to provide background damping to eliminate short spurious waves to prevent them from propagating across the computation domain. Generally speaking, small-amplitude short spurious waves are just low-level pollutants of the numerical solution, but if these waves are allowed to impinge on an internal or external boundary of the computational domain, they could lead to the reflection of large-amplitude long waves. These spurious long waves are sometimes not distinguishable from the physical solution and are, therefore, extremely undesirable. The second reason to add artificial selective damping is to stabilize the numerical solution at a discontinuity. The damping prevents the buildup of spurious short waves, which are generated by the discontinuity, and this promotes stability.
In the present problem, the forcing functions are discontinuous at the blade tip. Thus, in addition to the general background damping with an inverse mesh Reynolds number 0.05, extra damping is added around the blade tip region. The mesh-size-change interface and the external boundary of the computation domain are also a form of discontinuity. Extra damping is added around these boundaries as well. To impose extra damping, a distribution of inverse mesh Reynolds number in the form of a Gaussian function with a half-width of four mesh spacings normal to the boundary is used. The maximum of the Gaussian is on the discontinuity with an assigned value of 0.05. At the tip of the blade, where the forcing function is discontinuous, more damping is required. A maximum value of 0.75 is used instead.