Numerical modeling of submarine turbidity currents over erodible beds using unstructured grids

- A 2-D coupled numerical model is developed to simulate turbidity current over erodible bed with wetting and drying.
- A special discretization for bed-slope source term is developed in order to obtain the well-balanced property.
- Time step constraints are proposed to guarantee the non-negativity of computed fluid depth and sediment concentration.

Second-order central-upwind schemes proposed by Bryson et al. (2011) for the Saint-Venant system have two very attractive properties: well-balanced and positivity preserving, which are originally designed for constant fluid density and fixed beds in Bryson et al. (2011). For the turbidity current system with variable density over erodible beds, such desired properties can be obtained by developing a well-balanced and positivity preserving central-upwind scheme following the ideas in Bryson et al. (2011). To this end, in this paper, a coupled numerical model for two-dimensional depth-averaged turbidity current system over erodible beds is developed using finite volume method on triangular grids. The proposed numerical model is second-order accurate in space using piecewise linear reconstruction and third-order accurate in time using a strong stability preserving Runge-Kutta method. Applying the central-upwind method to estimate numerical fluxes through cell interfaces, the model can successfully deal with sharp gradients in turbidity flows. The developed numerical model can preserve the well-balanced property over irregular bottom, guarantee the non-negative turbidity current depth over erodible beds, and preserving the positivity of suspended sediment. These features of the developed numerical model and its robustness and accuracy are demonstrated in several numerical tests.