Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6892183 | Computers & Mathematics with Applications | 2018 | 24 Pages |
Abstract
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.
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Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
M. Rehan Saleem, Saqib Zia, Waqas Ashraf, Ishtiaq Ali, Shamsul Qamar,