High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition

Simulations of Turbulent Flows with Strong Shocks and Density Variations: Final Report

“…Finally, the Shock Fit code is based on the shock-fitting method of (77), which treats the shock as a sharp entity and solves the compressible Navier-Stokes equations in conservation form in the computational domain. The shock velocity and the flow variables behind the shock are obtained using the Rankine-Hugoniot relations coupled with a characteristic compatibility equation.…”

“…In the shock fitting approach, any scheme can be used to solve the governing equations in the computational domain. In the present calculations, a fifth-order accurate upwind finite difference scheme (77) is used to discretize the governing equations. Results are shown only for problems with initially well-defined shocks (Shu-Osher problem and shock-vorticity/entropy wave interaction), with a fixed set of coefficients.…”

Analysis of local defect correction and high-order compact finite differences

“…• High order compact upwind scheme of Zhong (5-point scheme [26]). This is the scheme (10)- (14), modified for the first derivative:…”

“…The iteration is as in Algorithm 1; the basic coarse grid problem, the local fine grid problem and the updated coarse grid problem are given by (26), (27) and (28), respectively.…”

“…In the past years, many upwind schemes were proposed. The main articles are [1,5,22,26]. The analysis of the stability of numerical boundary treatment for high order compact finite difference schemes was done in [15].…”