Technical noteExtension of a well-balanced central upwind scheme for variable density shallow water flow equations on triangular grids

- Solution of variable density shallow water equations is applied to triangular grid.
- New discretization of source term is proposed to maintain well-balance property.
- The central upwind scheme preserves positivity of the flow in depth and density.
- Accuracy of the scheme is tested by running various benchmark test cases.

In this paper, the central upwind scheme for variable density shallow water system of equations is extended to triangular discretization of the domain. In this scheme, the well-balanced and positivity preserving properties are maintained such that the large oscillations and noises are avoided in the solution. Furthermore, time-history of flow surface always remains non-negative throughout the simulations. Various properties of the scheme are validated using several benchmark data. Also, the accuracy and efficiency of the methodology are tested by comparing the results of the model to other complex scheme for some test cases. The method ensures high computational efficiency while maintaining the accuracy of the results and preserves two types of “lake at rest” steady states, and is oscillation free across the small density change.