Development and Application of Perfectly Matched Layer for Numerical Boundary Treatment

Abstract

This master’s-level thesis work had focused on the boundary treatments for computational fluid dynamics problems, especially those with unbounded domains. Therefore, it involved a rigorous literature survey on boundary treatment techniques. The primary interest in this effort was on one of the emerging concepts of boundary treatment for numerical schemes, namely the perfectly matched layer (PML) absorbing technique. PML equations were constructed in both Cartesian and generalized coordinate systems to widen its application in uniform and non-uniform grid structures. Throughout the study, Euler equations for perturbation equations linearized about a uniform mean flow were utilized, and flow that is parallel to an axis and flow that is at an arbitrary direction were considered. The PML formulation was validated and PML cases were simulated for a combination of absorbing coefficients and layer thickness in order to find the optimum performance of the technique. The results were analyzed, and the issues were documented. Furthermore, PML equations were constructed by splitting the velocity into three components. Discussion is provided on the need for a proper spacetime transformation, based on the literature study.