scholarly journals A well-balanced positivity-preserving central-upwind scheme for shallow water equations on unstructured quadrilateral grids

2016 ◽  
Vol 126 ◽  
pp. 25-40 ◽  
Author(s):  
Hamidreza Shirkhani ◽  
Abdolmajid Mohammadian ◽  
Ousmane Seidou ◽  
Alexander Kurganov
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Upwind Scheme ◽  
Positivity Preserving

Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

2014 ◽  
Vol 16 (5) ◽  
pp. 1323-1354 ◽  
Author(s):  
Manuel Jesús Castro Diaz ◽  
Yuanzhen Cheng ◽  
Alina Chertock ◽  
Alexander Kurganov
Keyword(s):  
Shallow Water ◽  
Numerical Method ◽  
Shallow Water Equations ◽  
Numerical Experiments ◽  
Operator Splitting ◽  
Finite Volume Methods ◽  
Splitting Methods ◽  
Upwind Scheme ◽  
Operator Splitting Methods ◽  
Numerical Approaches

AbstractIn this paper, we develop and study numerical methods for the two-mode shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407-432]. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerical approaches—two operator splitting methods (based on either Roe-type upwind or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme—and test their performance in a number of numerical experiments. The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method.

scholarly journals Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows

2016 ◽  
Vol 136 ◽  
pp. 193-206 ◽  
Author(s):  
Abdelaziz Beljadid ◽  
Abdolmajid Mohammadian ◽  
Alexander Kurganov
Keyword(s):  
Shallow Water ◽  
Upwind Scheme ◽  
Positivity Preserving ◽  
Water Flows ◽  
Shallow Water Flows
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