A coupled finite volume and material point method for two-phase simulation of liquid-sediment and gas-sediment flows

TL;DR

This paper introduces a hybrid simulation framework combining finite volume and material point methods to improve accuracy and stability in modeling complex two-phase flows involving liquids, gases, and sediments.

Contribution

It develops a coupled FVM-MPM approach that addresses numerical limitations of pure MPM in fluid simulations, enabling more reliable long-term simulations of liquid-sediment and gas-sediment flows.

Findings

Enhanced simulation stability over long durations

Reduced numerical errors compared to pure MPM

Effective modeling of complex two-phase flow phenomena

Abstract

Mixtures of fluids and granular sediments play an important role in many industrial, geotechnical, and aerospace engineering problems, from waste management and transportation (liquid--sediment mixtures) to dust kick-up below helicopter rotors (gas--sediment mixtures). These mixed flows often involve bulk motion of hundreds of billions of individual sediment particles and can contain both highly turbulent regions and static, non-flowing regions. This breadth of phenomena necessitates the use of continuum simulation methods, such as the material point method (MPM), which can accurately capture these large deformations while also tracking the Lagrangian features of the flow (e.g.\ the granular surface, elastic stress, etc.). Recent works using two-phase MPM frameworks to simulate these mixtures have shown substantial promise; however, these approaches are hindered by the numerical limitations of MPM when simulating pure fluids. In addition to the well-known particle ringing instability and difficulty defining inflow/outflow boundary conditions, MPM has a tendency to accumulate quadrature errors as materials deform, increasing the rate of overall error growth as simulations progress. In this work, we present an improved, two-phase continuum simulation framework that uses the finite volume method (FVM) to solve the fluid phase equations of motion and MPM to solve the solid phase equations of motion, substantially reducing the effect of these errors and providing better accuracy and stability for long-duration simulations of these mixtures.