Modifying and Reducing Numerical Dissipation in a Two-Dimensional Central-Upwind Scheme (Advances in Applied Mathematics and Mechanics, 2012)
This study presents a modification of the central-upwind Kurganovscheme for approximating the solution of the 2D Euler equation. The prototype,extended from a 1D model, reduces substantially less dissipation than expected.The problem arises from over-restriction of some slope limiters, which keep slopesbetween interfaces of cells to be Total-Variation-Diminishing. This study reports thedefect and presents a re-derived optimal formula. Numerical experiments highlightthe significance of this formula, especially in long-time, large-scale simulations.