# Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients

@article{Chertock2014CentralupwindSF, title={Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients}, author={Alina Chertock and Alexander Kurganov and Yu Liu}, journal={Numerische Mathematik}, year={2014}, volume={127}, pages={595-639} }

We introduce a central-upwind scheme for one- and two-dimensional systems of shallow-water equations with horizontal temperature gradients (the Ripa system). The scheme is well-balanced, positivity preserving and does not develop spurious pressure oscillations in the neighborhood of temperature jumps, that is, near the contact waves. Such oscillations would typically appear when a conventional Godunov-type finite volume method is applied to the Ripa system, and the nature of the oscillation is…

## 40 Citations

Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with variable density

- MathematicsArXiv
- 2022

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,…

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A Hybrid Method to Solve Shallow Water Flows with Horizontal Density Gradients

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It is shown that in some parameter regimes numerically recognizing such invariants across contact discontinuities is important to correctly compute the flow near those interfaces, and a numerical algorithm is presented that correctly captures all waves with a hybrid strategy.

An adaptive central‐upwind scheme on quadtree grids for variable density shallow water equations

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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.

The space-time CESE scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

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Well-Balanced Numerical Schemes for Shallow Water Equations with Horizontal Temperature Gradient

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A class of well-balanced numerical schemes for the one-dimensional shallow water equations with temperature gradient is constructed. The construction of the schemes is based on two steps: the first…

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

- PhysicsPloS one
- 2018

The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate and in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows

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Well-balanced central finite volume methods for the Ripa system

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Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Models

- Environmental ScienceJ. Sci. Comput.
- 2022

We extend recently proposed flux globalization based well-balanced path-conservative central-upwind schemes to several shallow water models including the Saint-Vevant system with and without the…

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