Name
Title | ||
|---|---|---|
Well-Balancing via Flux Globalization: Applications to Shallow Water Equations with Wet/Dry Fronts |
Abstract | ||
|---|---|---|
We study the flux globalization based central-upwind scheme from Cheng et al. (J Sci Comput 80:538-554, 2019) for the Saint-Venant system of shallow water equations. We first show that while the scheme is capable of preserving moving-water equilibria, it fails to preserve much simpler "lake-at-rest" steady states. We then modify the computation of the global flux variable and develop a well-balanced scheme, which can accurately handle both still- and moving-water equilibria. In addition, we extend the flux globalization based central-upwind scheme to the case when "dry" and/or "almost dry" areas are present. To this end, we introduce a hybrid approach: we use the flux globalization based scheme inside the "wet" areas only, while elsewhere we apply the central-upwind scheme from Bollermann et al. (J Sci Comput 56:267-290, 2013), which is designed to accurately capture wet/dry fronts. We illustrate the performance of the proposed schemes on a number of numerical examples. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1007/s10915-021-01680-z | JOURNAL OF SCIENTIFIC COMPUTING |
Keywords | DocType | Volume |
Flux globalization, Central-upwind schemes, Well-balanced schemes, "Lake-at-rest" steady states, "Dry lake" steady states | Journal | 90 |
Issue | ISSN | Citations |
1 | 0885-7474 | 0 |
PageRank | References | Authors |
0.34 | 0 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alina Chertock | 1 | 10 | 2.92 |
| Alexander Kurganov | 2 | 0 | 0.34 |
| Xin Liu | 3 | 0 | 0.34 |
| Yongle Liu | 4 | 0 | 0.34 |
| Tong Wu | 5 | 0 | 0.34 |