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

Abstract

Many landslides in nature may be classified as deformable landslides. The landslide volume is usually modeled as a rheological material when SPH methods are used for landslide simulation, since these methods allow for the use of particles with different fluid properties. To increase the accuracy, the Carreau-Yasuda model is chosen in this study to predict the behavior of the rheological material. This rheological model overcomes the weakness of the power-law model in predicting the viscosity at zero and infinite shear strain rates. Also, a fully explicit three-step algorithm is proposed to solve the governing equations. In the first step, the momentum equation is solved in the presence of the body forces while neglecting all other forces. In this step intermediate velocity values are computed. In the second step, the calculated intermediate velocities are employed to compute divergence of the stress tensor, and velocity components of each particle are updated to find their intermediate positions. These two steps are called predictor steps. In the third, corrector step, the pressure gradient in the momentum equation is merged with the continuity equation, and lastly the final particle velocity is calculated at the end of the time step. The fully explicit three-step algorithm is used in combination with Carreau-Yasuda model to simulate the submarine non-rigid landslide from the physical model. The comparison with the experimental data indicates good agreement between the calculated and observed water surface elevations with very low L2 relative error norm (L2) and RMSE values that 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, the shape and the advancement of the non-rigid body made of sand are captured equally good.