Development of perfectly matched layer numerical boundary condition in a generalized coordinate system
The research activity leading to this dissertation focused on the boundary treatment for computational fluid dynamics problems, especially those with unbounded domains. This involved a rigorous literature survey of boundary treatment techniques. The primary interest of this effort was on one of the emerging concepts of nonreflecting boundary treatment for numerical schemes, namely the perfectly matched layer (PML) absorbing technique. The need for an appropriate space-time transformation for a stable PML emphasized in previous efforts was the starting point for this developmental research activity. Based on this, unsplit PML equations were constructed for Euler equations linearized over a uniform mean flow with a proper space-time transformation. Dispersion analysis was carried out to demonstrate the effectiveness of the space-time transformation in terms of stability of the PML formulation. Numerous numerical simulations were carried out to investigate the stability of the PML formulation for long-term integration of various combinations of time-step size and PML parameters. The major focus of this research was to extend the construction of the PML for nonlinear Euler equations in a generalized coordinate system to widen its application in uniform and nonuniform grid structures. Emphasis was placed on the application of conventional numerical schemes without employing any form of artificial dissipation or numerical filtering. With this objective in mind, the split-form PML equations for nonlinear Euler equations were constructed. Various numerical simulations were carried out to validate the PML formulation and demonstrate its effectiveness as an absorbing boundary condition.
Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Aerospace Engineering.