Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with variable density
@article{Nguyen2022AdaptiveCS, title={Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with variable density}, author={Thuong X. Nguyen}, journal={ArXiv}, year={2022}, volume={abs/2201.10073} }
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, positivity-preserving, and oscillation free at the curve where two types of fluid merge. The proposed approach is an extension of the adaptive well-balanced, positivity-preserving scheme developed in Epshteyn and Nguyen (arXiv preprint arXiv:2011.06143, 2020). In particular, to preserve “lake-at-rest…
References
SHOWING 1-10 OF 48 REFERENCES
An adaptive central‐upwind scheme on quadtree grids for variable density shallow water equations
- Computer ScienceInternational Journal for Numerical Methods in Fluids
- 2022
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.
Adaptive Central-Upwind Scheme on Triangular Grids for the Saint-Venant System
- Computer ScienceArXiv
- 2020
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
- Computer ScienceComputers & Fluids
- 2020
Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients
- PhysicsNumerische Mathematik
- 2014
A central-upwind scheme for one- and two-dimensional systems of shallow-water equations with horizontal temperature gradients (the Ripa system) is introduced, which is highly accurate, preserves two types of “lake at rest” steady states, and is oscillation free across the temperature jumps.
Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids
- Computer ScienceSIAM J. Sci. Comput.
- 2005
A two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes and notes in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes.
Well-balanced positivity preserving central-upwind scheme with a novel wet/dry reconstruction on triangular grids for the Saint-Venant system
- MathematicsJ. Comput. Phys.
- 2018
A well-balanced positivity-preserving central-upwind scheme for shallow water equations on unstructured quadrilateral grids
- Mathematics
- 2016
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
- Mathematics
- 2011
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…
Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes
- MathematicsJ. Sci. Comput.
- 2013
The simple positivity-preserving limiter is reformulated, and it is proved that the resulting scheme guarantees the positivity of the water depth, as well as well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.
Well-Balanced Adaptive Mesh Refinement for shallow water flows
- Computer ScienceJ. Comput. Phys.
- 2014