• Corpus ID: 246276221

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
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.
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.
Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients
TLDR
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
TLDR
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.
Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes
TLDR
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.
Finite-volume schemes for shallow-water equations
TLDR
This paper focuses on central-upwind schemes, which belong to the family of Godunov-type Riemann-problem-solver-free central schemes, but incorporate some upwinding information about the local speeds of propagation, which helps to reduce an excessive amount of numerical diffusion typically present in classical (staggered) non-oscillatory central schemes.
...
...