Numerical simulation of submarine landslide tsunamis based on the smoothed particle hydrodynamics model

This paper establishes a SPH (Smoothed Particle Hydrodynamics) model for simulating underwater landslides based on the mixture theory. This model requires only one layer of particles, which greatly improves the computational efficiency compared with the traditional two-layer particle simulation for a mixture theory scheme. In the numerical model, based on a mixture theory, submerged landslide flow is regarded as a mixture of water and sediment phases and is discretized into a series of SPH mixed particles employing the volume fraction of the sediment phase. Using this volume fraction, a convection-diffusion term is calculated to represent the material transport between the water phase and the sediment phase. In addition, based on this volume fraction, the SPH mixed particles at any location in the considered domain are classified into three categories: (i) pure water, (ii) low-concentration suspended sediment, and (iii) high-concentration sediment. Pure water is treated as a Newtonian fluid. High-concentration sediment is modeled as a non-Newtonian fluid, and the Herschel-Bulkley-Papanastasiou rheological model is used to describe the viscous forces. The viscosity of the low-concentration suspended sediment, which acts as a transition layer between pure water and high-concentration sediment, is derived from the Chezy relation. A comparison of the numerical and experimental results demonstrates the high accuracy of the present numerical scheme. Using this validated numerical model, underwater landslides are simulated. Specifically, the effects of landslide deformation and compaction degree on the amplitudes of the surge wave crest and trough are investigated.