A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients
| Autor: | Shamsul Qamar, Ishtiaq Ali, M. Rehan Saleem, Waqas Ashraf, Saqib Zia |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Shallow Water
Geological Phenomena Oceans and Seas Temperature Gradients Velocity Kinetic scheme lcsh:Medicine Fluid Mechanics 010103 numerical & computational mathematics Continuum Mechanics 01 natural sciences Perturbation (Geology) Motion Robustness (computer science) Fluid dynamics Computer Simulation 0101 mathematics lcsh:Science Fluid Flow Shallow water equations Eigenvalues and eigenvectors Mathematics Sedimentary Geology Multidisciplinary Physics Numerical analysis lcsh:R Temperature Water Classical Mechanics Eigenvalues Geology Fluid Dynamics Mechanics Models Theoretical 010101 applied mathematics Kinetics Waves and shallow water Temperature gradient Algebra Linear Algebra Physical Sciences Hydrodynamics Earth Sciences Thermodynamics lcsh:Q Hydrology Research Article |
| Zdroj: | PLoS ONE, Vol 13, Iss 5, p e0197500 (2018) PLoS ONE |
| ISSN: | 1932-6203 |
| Popis: | This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme. |
| Databáze: | OpenAIRE |
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