scholarly journals Central-Upwind Scheme on Triangular Grids for the Saint-Venant System of Shallow Water Equations

2011 ◽  
Author(s):  
Steve Bryson ◽  
Yekaterina Epshteyn ◽  
Alexander Kurganov ◽  
Guergana Petrova ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Upwind Scheme ◽  
Triangular Grids

scholarly journals Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Sudi Mungkasi
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Error Indicator ◽  
Triangular Grids ◽  
Volume Method ◽  
Numerical Entropy

This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.

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 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
Sign in / Sign up

Export Citation Format

Share Document