摘要
In order to suppress the failure of preserving positivity of density or pres-sure,a positivity-preserving limiter technique coupled with h-adaptive Runge-Kutta discontinuous Galerkin(RKDG)method is developed in this paper.Such a method is implemented to simulate flows with the large Mach number,strong shock/obstacle interactions and shock diffractions.The Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is also presented.This ap-proach directly uses the cell solution polynomial of DG finite element space as the interpolation formula.The method is validated by the well documented test ex-amples involving unsteady compressible flows through complex bodies over a large Mach numbers.The numerical results demonstrate the robustness and the versatility of the proposed approach.
基金
supported by the National Science Foundation of China(Nos.11102179,91230110,11328104)
PhD Studentship from De Montfort University of UK.