The space–time CESE scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients
| Autor: | Ishtiaq Ali, Waqas Ashraf, Shamsul Qamar, Saqib Zia, M. Rehan Saleem |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Scheme (programming language)
Mathematical optimization Space time 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics Nonlinear system Waves and shallow water Computational Theory and Mathematics Modeling and Simulation Applied mathematics 0101 mathematics Differential (infinitesimal) Element (category theory) computer Shallow water equations computer.programming_language Variable (mathematics) Mathematics |
| Zdroj: | Computers & Mathematics with Applications. 75:933-956 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2017.10.021 |
| Popis: | The effects of bottom topography and horizontal temperature gradients on the shallow water flows are theoretically investigated. The considered systems of partial differential equations (PDEs) are non-strictly hyperbolic and non-conservative due to the presence of non-conservative differential terms on the right hand side. The solutions of these model equations are very challenging for a numerical scheme. Thus, our primary goal is to introduce an improved numerical scheme which can handle the non-conservative differential terms efficiently and accurately. In this paper, the space–time conservation element and solution element (CESE) method is extended to approximate these model equations. The proposed scheme has capability to overcome all difficulties posed by this nonlinear system of PDEs. The performance of the scheme is analyzed by considering several case studies of practical interest and the results of suggested scheme are compared with those of central NT scheme. The accuracy of the scheme is verified qualitatively and quantitatively. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect