A consistent multi-resolution particle method for fluid-driven granular dynamics

Abstract

Granular dynamics driven by fluid flow is ubiquitous in many industrial and natural processes, such as fluvial and coastal sediment transport. Yet, their complex multiphysics and multi-scale nature challenge numerical models’ accuracy and efficiency. Here, we develop a new multi-resolution mesh-free particle method, based on an enhanced weakly-compressible Moving Particle Semi-implicit (MPS) method, to study the dynamics of rapid fluid-driven granular erosion. We propose and validate a novel multi-resolution multiphase MPS formulation for the consistent and conservative form of the governing equations, including particle stabilization techniques. First, we discuss the numerical accuracy and convergence of the proposed approximation operators through two numerical benchmark cases: the multi-viscosity Poiseuille flow and the multi-density hydrostatic pressure. Then, coupling the developed model with a generalized rheology equation, we investigate the water dam-break waves over movable beds. The particle convergence study confirms that the proposed multi-resolution formulation predicts the analytical solutions with acceptable accuracy and order of convergence. Validating the multiphase granular flow reveals that the mechanical behavior of this fluid-driven problem is highly sensitive to the water-sediment density ratio; the bed with lighter grains experiences extreme erosion and interface deformations. For the bed with a heavier material but different geometrical setups, the surge speed, and the transport layer thickness remain almost identical (away from the gate). Furthermore, while the multi-resolution model accurately estimates the global sediment dynamics, the single-resolution model underestimates the flow evolution. Overall, the qualitative and quantitative analysis of results emphasizes the importance of multi-scale multi-density interactions in fluid-driven modeling.