Enhanced granular dynamics modelling with stabilised and noise-reduced pressure using weakly compressible smoothed particle hydrodynamics

This paper presents a robust and effective weakly compressible smoothed particle hydrodynamics (WCSPH) model for simulating granular flow. The model incorporates a well-structured viscoplastic non-Newtonian μ ( I ) framework to accurately represent the behaviour of particulate materials. To precisely compute the pressure in the solid phase, the pore water pressure is determined using the same methodology as fluid pressure, based on the continuity equations governing pore water. Additionally, an extended extrapolation boundary condition is applied for two-phase granular flow, which extrapolates sediment and fluid particle properties from dynamic particles at varying distances from the wall boundaries to the relevant ghost particles using a first-order Taylor series expansion. This approach effectively mitigates unphysical fluctuations and numerical noise at the boundaries, eliminating the need for additional diffusive treatments beyond the δ -SPH term and the so-called mirror particles that are commonly required in existing two-phase meshless methods. The performance of the proposed method is assessed through a suite of challenging two-phase granular benchmark cases, including two-layer Poiseuille flow, a hydrostatic wedge test, dam-break flow over a movable bed, immersed landslide motion, and three-dimensional submerged granular dam failure. The numerical results are systematically compared to experimental measurements, analytical solutions, and alternative meshless formulations, demonstrating the superior accuracy and robustness of the proposed approach.