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 - <p style="text-align: justify;">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.</p>