scholarly journals A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations

2022 ◽  
Vol 31 (1) ◽  
pp. 94-130
Author(s):  
Min Zhang
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Moving Mesh ◽  
Positivity Preserving ◽  
Dg 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

On a Moving Mesh Method Applied to the Shallow Water Equations

2010 ◽  
Author(s):  
J. Felcman ◽  
L. Kadrnka ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Moving Mesh ◽  
Moving Mesh Method ◽  
Mesh Method

scholarly journals Enriched Galerkin method for the shallow-water equations

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Moritz Hauck ◽  
Vadym Aizinger ◽  
Florian Frank ◽  
Hennes Hajduk ◽  
Andreas Rupp
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Lower Number ◽  
Approximation Spaces ◽  
Continuous Galerkin ◽  
Dg Method ◽  
Implementation Aspects ◽  
Locally Conservative

AbstractThis work presents an enriched Galerkin (EG) discretization for the two-dimensional shallow-water equations. The EG finite element spaces are obtained by extending the approximation spaces of the classical finite elements by discontinuous functions supported on elements. The simplest EG space is constructed by enriching the piecewise linear continuous Galerkin space with discontinuous, element-wise constant functions. Similar to discontinuous Galerkin (DG) discretizations, the EG scheme is locally conservative, while, in multiple space dimensions, the EG space is significantly smaller than that of the DG method. This implies a lower number of degrees of freedom compared to the DG method. The EG discretization presented for the shallow-water equations is well-balanced, in the sense that it preserves lake-at-rest configurations. We evaluate the method’s robustness and accuracy using various analytical and realistic problems and compare the results to those obtained using the DG method. Finally, we briefly discuss implementation aspects of the EG method within our MATLAB / GNU Octave framework FESTUNG.

scholarly journals An adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations

2020 ◽  
Vol 208 ◽  
pp. 104633
Author(s):  
Mohammad A. Ghazizadeh ◽  
Abdolmajid Mohammadian ◽  
Alexander Kurganov
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Upwind Scheme ◽  
Positivity Preserving
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