Compact Difference Methods for Discharge Modeling in Aerodynamics

Abstract

This paper explores the feasibility of applying high-order, compact difference methods to the modeling of glow discharges for high-speed flow control. Previous papers (AIAA 2008-1357) have successfully applied second-order finite difference methods to glow discharge modeling. Detailed grid resolution studies, however, have revealed that very fine grid resolution is required for acceptable quantitative results. High-order compact difference methods offer a possible means of achieving high spatial accuracy on coarser grids, potentially leading to a significant reduction in the computational cost of an accurate solution. In previous work (AIAA 2009-1047), preliminary, one-dimensional compact difference calculations were carried out for glow discharge problems. Here the work is extended to two dimensions. Sample compact difference calculations are presented for several test cases, including a Poisson equation solution, a compressible Couette flow problem, a hypersonic laminar boundary layer flow, and a transient plasma-sheath problem. Spatial convergence of secondthrough sixth-order compact schemes was investigated, and found to be comparable to the theoretical order of accuracy. In particular, compact difference methods of up to sixth order can successfully achieve their theoretical order of accuracy for the coupled Poisson and Euler equations with source terms. Compact difference schemes appear to be a promising numerical approach for modeling plasma actuators for high-speed flow control.