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Volume 4, Issue 3
Modifying and Reducing Numerical Dissipation in a Two-Dimensional Central-Upwind Scheme

Chi-Jer Yu & Chii-Tung Liu

DOI: 10.4208/aamm.10-m11142

Adv. Appl. Math. Mech., 4 (2012), pp. 340-353.

Published online: 2012-04

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  • Abstract

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.

  • Keywords

Hyperbolic systems of conservation laws, Godunov-type finite-volume methods, central-upwind scheme, Kurganov, numerical dissipation, anti-diffusion.

  • AMS Subject Headings

76T05, 65M05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-340, author = {Yu , Chi-Jer and Liu , Chii-Tung}, title = {Modifying and Reducing Numerical Dissipation in a Two-Dimensional Central-Upwind Scheme}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {3}, pages = {340--353}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m11142}, url = {http://global-sci.org/intro/article_detail/aamm/123.html} }
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.

Yu , Chi-Jer and Liu , Chii-Tung. (2012). Modifying and Reducing Numerical Dissipation in a Two-Dimensional Central-Upwind Scheme. Advances in Applied Mathematics and Mechanics. 4 (3). 340-353. doi:10.4208/aamm.10-m11142
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