How to ensure stability and conservative solution in a simple way in application of the overlapping grid methods in computational fluid dynamics

摘要

The overlapping grid methods play an important role in Applied Computational Fluid Dynamics (CFD). Stability is absolutely necessary for the method to work. Conservation was believed to be important for computing shock waves. However, a conservative interpolation based on the complicated flux interpolation is unstable in the sense of Gustafsson, Kreiss, and Sundstrom. Based on a nonlinear analysis for the interaction between shock waves and grid interfaces, three sufficient conditions ensuring conservative solutions are derived. Based on the analysis, it is concluded that using a nonconservative normal interpolation and an internal difference approximation no less dissipative than the Roe scheme at shock positions, the overlapping grid method yields conservative results in a stable and convergent way. The questions of accuracy, convergence to steady state, and solution uniqueness are also discussed.