2D Well-balanced Positivity Preserving Shallow Flow Model with Wetting and Drying on Triangular Grids

In the framework of Godunov-type finite volume method, this paper presents a two dimensional (2-D) well-balanced shallow flow model with wetting and drying on triangular grids. The model uses central upwind scheme, which is a type of Riemann-solver-free method for hyperbolic conservation laws, to compute mass and momentum flux at interface. A multidimensional slope limiter is introduced to achieve second-order accuracy in space and prevent numerical oscillations. The bed slope source term is discretized reasonably to exactly balance numerical flux at stationary flow condition, and guarantee the well-balanced property of the scheme. The reconstruction method adopted in the present model ensures non-negative reconstructed water depth and resolves the stationary or wet/dry front, and friction term is solved by semi-implicit scheme to ensure the stability of the model. The developed model is capable of being well-balanced and preserving the computed water depth to be non-negative, which make it robust and stable to simulate shallow flows over complex irregular terrain. Two benchmark tests, an experimental case and a field-scale application are simulated to verify the well-balanced property, positivity preserving property, high accuracy and robustness of proposed model.