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

@article{Shirkhani2016AWP,
  title={A well-balanced positivity-preserving central-upwind scheme for shallow water equations on unstructured quadrilateral grids},
  author={Hamidreza Shirkhani and Abdolmajid Mohammadian and Ousmane Seidou and Alexander Kurganov},
  journal={Computers \& Fluids},
  year={2016},
  volume={126},
  pages={25-40}
}
Adaptive Central-Upwind Scheme on Triangular Grids for the Saint-Venant System
TLDR
A robust adaptive well-balanced and positivity-preserving central-upwind scheme on unstructured triangular grids for shallow water equations and obtains local a posteriori error estimator for the efficient mesh refinement strategy.
An adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations
Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with variable density
In this paper, we construct a robust adaptive central-upwind scheme on unstructured triangular grids for two-dimensional shallow water equations with variable density. The method is wellbalanced,
An adaptive central‐upwind scheme on quadtree grids for variable density shallow water equations
TLDR
An adaptive scheme on quadtree grids for variable density shallow water equations and a scheme for the coupled system is developed, capable of exactly preserving “lake‐at‐rest” steady states.
Well-Balanced Numerical Method for Atmospheric Flow Equations with Gravity
We are interested in simulating gravitationally stratified atmospheric flows governed by the compressible Euler equations in irregular domains. In such simulations, one of the challenges arises when
...
...

References

SHOWING 1-10 OF 45 REFERENCES
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states
A Survey of High Order Schemes for the Shallow Water Equations
In this paper, we survey our recent work on designing high order positivity- preserving well-balanced finite difference and finite volume WENO (weighted essen- tially non-oscillatory) schemes, and
An unstructured grid, three‐dimensional model based on the shallow water equations
TLDR
A semi-implicit finite difference model based on the three-dimensional shallow water equations is modified to use unstructured grids, which is relatively simple, conserves mass, can fit complicated boundaries and yet is sufficiently flexible to permit local mesh refinements in areas of interest.
A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗
A family of Godunov-type central-upwind schemes for the Saint-Venant system of shallow water equations has been first introduced in (A. Kurganov and D. Levy, M2AN Math. Model. Numer. Anal., 36,
...
...