TY - JOUR T1 - Modifying and Reducing Numerical Dissipation in a Two-Dimensional Central-Upwind Scheme AU - Yu , Chi-Jer AU - Liu , Chii-Tung JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 340 EP - 353 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m11142 UR - https://global-sci.org/intro/article_detail/aamm/123.html KW - Hyperbolic systems of conservation laws, Godunov-type finite-volume methods, central-upwind scheme, Kurganov, numerical dissipation, anti-diffusion. AB -

This study presents a modification of the central-upwind Kurganov scheme 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 slopes between interfaces of cells to be Total-Variation-Diminishing. This study reports the defect and presents a re-derived optimal formula. Numerical experiments highlight the significance of this formula, especially in long-time, large-scale simulations.