Flux limiting with high-order compact schemes - Mawlood M.K.; Basri S.; Mokhtar A.S.; Ahmad M.M.H.M.; Asrar W.; Omar A.A. (2023)
In this paper, we present a modified flux limiter for limiting the numerical flux differences obtained from a fifth-order upwind compact scheme. The accuracy of the scheme is tested through the solution of the scalar 1D inviscid Burgers equation. The method is then used for solving the 2D Euler equations for flows containing shocks. For unsteady problems, a multistage SSP Runge-Kutta method is employed for the time integration. For two-dimensional steady-state solutions, first-order implicit time integration, with LU decomposition, is employed. Results have shown that the developed flux limiter significantly eliminates the numerical oscillations. Copyright 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.