Numerical simulation of Submarine non-rigid landslide by an explicit three-step incompressible smoothed particle hydrodynamics

Deformable landslide body is modeled as a rheological material when SPH methods are used for numerical simulations. To increase accuracy, Carreau-Yasuda rheological model is chosen in this study. The model overcomes the weakness of the power-law model in predicting viscosity at zero and infinite shear strain rates. Also, a fully explicit three-step algorithm is proposed to solve governing equations. In the first step , intermediate velocities are computed in the presence of body forces. In the second step , they are used to compute divergence of stress tensor and to find intermediate particle positions. In the third step , pressure gradient in the momentum equation is merged with the continuity equation, and final particle velocity is calculated at the end of the time step. The algorithm is used in combination with Carreau-Yasuda model to simulate submarine non-rigid landslide. Comparison with experimental data indicates good agreement between calculated and observed water surface elevations with very low L2 relative error norm(epsilon(L2)) and RMSE values. They are up to 70% lower than those from previous studies when Cross and Bingham rheological models were used with ISPH and WCSPH models, respectively. Moreover, shape and advancement of the non-rigid body made of sand are well captured.