Explicit Expression of Weighting Factor for Improved Estimation of Numerical Flux in Local-inertial Models

Two-dimensional shallow water models have been widely used in forecasting, risk assessment and management of floods. Application of these models to large-scale floods with high-resolution terrain data significantly increases the computation cost. In order to reduce computation time, shallow water models are simplified by neglecting the inertial and/or convective acceleration terms in the momentum equations. The local-inertial models have proved to significantly improve the computational efficiency even for large scale flood forecasting. However, instability issues are encountered on smooth surfaces of urban areas having low friction values. This problem was resolved by de Almeida et al. (Water Resources Research 48: 1 - 14, 2012) by introducing limited artificial diffusion in the form of weighting factors for the neighboring fluxes. The arbitrary value of the weighting factor poses a practical limitation of being case specific and requiring calibration for accurate solutions. This study derives an explicit expression for the weighting factor, an adaptive formulation dependent on local velocity, flow depth, grid and time step size, that eliminates the need for trials and approximations. Comparisons between analytical, experimental and real-world applications confirm the accuracy and robustness of the proposed weighting factor. Implementation of adaptive weights results in less computation time compared to LISFLOOD-FP (~1.2 times) and hold a significant advantage over HEC-RAS (~25.9 times) as it allows the use of larger time step at higher CFL values. The contribution of the present study therefore resolves an important problem of current large scale flood simulations, especially those implemented in real-time.