The space–time CESE scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2017.10.021 ◽

2018 ◽

Vol 75 (3) ◽

pp. 933-956

Author(s):

M. Rehan Saleem ◽

Saqib Zia ◽

Waqas Ashraf ◽

Ishtiaq Ali ◽

Shamsul Qamar

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Bottom Topography ◽

Temperature Gradients ◽

Variable Bottom ◽

Horizontal Temperature Gradients

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A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

PLoS ONE ◽

10.1371/journal.pone.0197500 ◽

2018 ◽

Vol 13 (5) ◽

pp. e0197500

Author(s):

M. Rehan Saleem ◽

Waqas Ashraf ◽

Saqib Zia ◽

Ishtiaq Ali ◽

Shamsul Qamar

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Bottom Topography ◽

Temperature Gradients ◽

Splitting Scheme ◽

Flux Vector ◽

Variable Bottom ◽

Flux Vector Splitting ◽

Horizontal Temperature Gradients

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Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients

Numerische Mathematik ◽

10.1007/s00211-013-0597-6 ◽

2013 ◽

Vol 127 (4) ◽

pp. 595-639 ◽

Author(s):

Alina Chertock ◽

Alexander Kurganov ◽

Yu Liu

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Temperature Gradients ◽

Upwind Schemes ◽

Horizontal Temperature Gradients

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The Riemann problem for the shallow water equations with horizontal temperature gradients

Applied Mathematics and Computation ◽

10.1016/j.amc.2017.12.031 ◽

2018 ◽

Vol 325 ◽

pp. 159-178

Author(s):

Mai Duc Thanh

Keyword(s):

Shallow Water ◽

Riemann Problem ◽

Shallow Water Equations ◽

Temperature Gradients ◽

Horizontal Temperature Gradients

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Lie symmetries of two-dimensional shallow water equations with variable bottom topography

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/5.0007274 ◽

2020 ◽

Vol 30 (7) ◽

pp. 073132

Author(s):

Alexander Bihlo ◽

Nataliia Poltavets ◽

Roman O. Popovych

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Bottom Topography ◽

Lie Symmetries ◽

Two Dimensional ◽

Variable Bottom

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Zeroth‐order conservation laws of two‐dimensional shallow water equations with variable bottom topography

Studies in Applied Mathematics ◽

10.1111/sapm.12320 ◽

2020 ◽

Vol 145 (2) ◽

pp. 291-321

Author(s):

Alexander Bihlo ◽

Roman O. Popovych

Keyword(s):

Conservation Laws ◽

Shallow Water ◽

Shallow Water Equations ◽

Bottom Topography ◽

Two Dimensional ◽

Zeroth Order ◽

Variable Bottom

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A space–time CESE scheme for shallow water magnetohydrodynamics equations with variable bottom topography

Journal of the Brazilian Society of Mechanical Sciences and Engineering ◽

10.1007/s40430-016-0678-4 ◽

2016 ◽

Vol 39 (5) ◽

pp. 1563-1573 ◽

Author(s):

M. Rehan Saleem ◽

Saqib Zia ◽

Shamsul Qamar

Keyword(s):

Shallow Water ◽

Bottom Topography ◽

Magnetohydrodynamics Equations ◽

Variable Bottom ◽

Shallow Water Magnetohydrodynamics

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Common Hamiltonian structure of the shallow water equations with horizontal temperature gradients and magnetic fields

Physics of Fluids ◽

10.1063/1.1530576 ◽

2003 ◽

Vol 15 (2) ◽

pp. 292-297 ◽

Author(s):

Paul J. Dellar

Keyword(s):

Magnetic Fields ◽

Shallow Water ◽

Shallow Water Equations ◽

Hamiltonian Structure ◽

Temperature Gradients ◽

Horizontal Temperature Gradients

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Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography

Networks and Heterogeneous Media ◽

10.3934/nhm.2016.11.145 ◽

2016 ◽

Vol 11 (1) ◽

pp. 145-162 ◽

Author(s):

Andreas Hiltebrand ◽

Siddhartha Mishra

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Bottom Topography ◽

Entropy Stability

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A well-balanced high-order scheme on van Leer-type for the shallow water equations with temperature gradient and variable bottom topography

Advances in Computational Mathematics ◽

10.1007/s10444-020-09832-9 ◽

2021 ◽

Vol 47 (1) ◽

Author(s):

Nguyen Xuan Thanh ◽

Mai Duc Thanh ◽

Dao Huy Cuong

Keyword(s):

Temperature Gradient ◽

Shallow Water ◽

Shallow Water Equations ◽

Bottom Topography ◽

High Order Scheme ◽

Variable Bottom ◽

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Numerical solution of the two-layer shallow water equations with bottom topography

Journal of Marine Research ◽

10.1357/002224002762324194 ◽

2002 ◽

Vol 60 (4) ◽

pp. 605-638 ◽

Author(s):

Rick Salmon

Keyword(s):

Numerical Solution ◽

Shallow Water ◽

Shallow Water Equations ◽

Bottom Topography

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