Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock. Issue 1 (15th February 2016)

• Record Type: Journal Article
• Authors: Liu, Jianming; Qiu, Jianxian; Goman, Mikhail; Li, Xinkai; Liu, Meilin
• Is Part Of: Numerical mathematics. Volume 9:Issue 1(2016)
• Page Start: 87
• Page End: 110
• Publication Date: 2016-02-15
• Subjects: 65M50, -- 65M60, -- 76L05; Discontinuous Galerkin method, -- adaptive Cartesian grid, -- positivity-preserving, -- immersed boundary method, -- complex geometry; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2015.m1416
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: In order to suppress the failure of preserving positivity of density or pressure, 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 approach directly uses the cell solution polynomial of DG finite element space as the interpolation formula. The method is validated by the well documented test examples 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.