On the Reduction of Numerical Dissipation in Central-Upwind Schemes
By Alexander Kurganov, Chi-Tien Lin. Communications in Computational Physics, 2007
209 citations recorded by the source corpus.
We study central-upwind schemes for systems of hyperbolic conservation laws, recently introduced in [13]. Similarly to staggered non-oscillatory central schemes, these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution, simplicity, universality and robustness. At the same time, the central-upwind framework allows one to decrease a relatively large amount of numerical dissipation present at the staggered central schemes. In this paper, we present a modification of the one-dimensional fullyand semi-discrete central-upwind schemes, in which the numerical dissipation is reduced even further. The goal is achieved by a more accurate projection of the evolved quantities onto the original grid. In the semi-discrete case, the reduction of dissipation procedure leads to a new, less dissipative numerical flux. We also extend the new semi-discrete scheme to the two-dimensional case via the rigorous, genuinely multidimensional derivation. The new semi-discrete schemes are tested on a number of numerical examples, where one can observe an improved resolution, especially of the contact waves.
Subfields: Atmospheric Science, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/386b9ab17d53c22839ee88acf6f7ed625d1a8167
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In Atmospheric Science
- Alina Chertock
- Tong Wu
- Henry G. Weller
- J. Reese
- Shumo Cui
- Luca Gasparini
- C. J. Greenshields
- Alexander Kurganov
In Computational Mechanics
- Alexander Kurganov
- Henry G. Weller
- J. Reese
- Luca Gasparini
- C. J. Greenshields
- Alina Chertock
- Tong Wu
- Shumo Cui
Citations in the corpus
- Implementation of semi‐discrete, non‐staggered central schemes in a colocated, polyhedral, finite volume framework, for high‐speed viscous flows (2009, methodology): “The method has been developed for multidimensional systems and unstructured meshes, principally using vertexstaggered (or overlapping) meshes of triangles [10, 11, 12, 13, 14, 15, 16], tetrahedra [17, 18], quadrilaterals [13, 19, 20, 21, 16, 22, 23, 24] and hexahedra [25].”
- Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes (2006, background): “Recent work on reduction of numerical dissipation in central-upwind schemes can be found in [20].”
- Path-conservative central-upwind schemes for nonconservative hyperbolic systems (2019, background): “, [30, 32, 34, 37, 38]) typically present in staggered central schemes such as the Nessyahu-Tadmor scheme [52] and its higher-order (see, e.”
- Well‐balanced positivity preserving central‐upwind scheme for the shallow water system with friction terms (2015, methodology): “Central-upwind schemes have been proposed for general hyperbolic system of conversation law in [16, 17, 20, 21] and extended to the Saint-Venant system and related models in [15,18,19].”