A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.
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...
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doaj-6151367a500149739038490e285ded512020-11-25T01:45:53ZengPublic Library of Science (PLoS)PLoS ONE1932-62032018-01-01135e019750010.1371/journal.pone.0197500A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.M Rehan SaleemWaqas AshrafSaqib ZiaIshtiaq AliShamsul QamarThis 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.http://europepmc.org/articles/PMC5979031?pdf=render |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
M Rehan Saleem Waqas Ashraf Saqib Zia Ishtiaq Ali Shamsul Qamar |
spellingShingle |
M Rehan Saleem Waqas Ashraf Saqib Zia Ishtiaq Ali Shamsul Qamar A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients. PLoS ONE |
author_facet |
M Rehan Saleem Waqas Ashraf Saqib Zia Ishtiaq Ali Shamsul Qamar |
author_sort |
M Rehan Saleem |
title |
A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients. |
title_short |
A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients. |
title_full |
A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients. |
title_fullStr |
A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients. |
title_full_unstemmed |
A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients. |
title_sort |
kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients. |
publisher |
Public Library of Science (PLoS) |
series |
PLoS ONE |
issn |
1932-6203 |
publishDate |
2018-01-01 |
description |
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. |
url |
http://europepmc.org/articles/PMC5979031?pdf=render |
work_keys_str_mv |
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