Robust coupled fluid‐particle simulation scheme in Stokes‐flow regime: Toward the geodynamic simulation including granular media

Abstract

We present a simulation scheme for solving high-viscosity fluid and particle dynamics in a coupled computational fluid dynamics and discrete element method (CFD-DEM) framework. This simulation scheme is intended to be used for geodynamical magmatic studies such as crystal settling at the melting roof of a magma chamber. The high-viscosity fluid is treated by the Stokes-flow approximation, where the fluid interacts with particles via the drag force in a cell-averaged manner. The particles are tracked with contact forces by DEM. To efficiently solve such Stokes-DEM coupled equations, we propose two key techniques. One is formulation of particle motion without the inertial term, allowing a larger time step at higher viscosities. The other is a semi-implicit treatment of the cell-averaged particle velocity in the fluid equation to stabilize the calculation. We simulate the settling particles in strongly viscous fluids in three dimensions and compare the results with the experimental and theoretical results. Our solution strategy is found to be robust and successfully captures the collective behavior of the particles. The simulation method presented here will be useful in various fields interested in long-term dynamics of high-viscosity granular media.

Silicic magma reservoirs in the Earth’s crust

“…Several "granular" multiphase models have been developed over the last decade to study magma dynamics. For example, multiphase fluid dynamics modeling where crystals are introduced using the discrete element method (DEM) coupled to Stokes flow solvers has been applied to magma chamber dynamics recently by Furuichi and Nishiura (2014) and Bergantz et al (2015), considering mostly how crystal melt mechanical interactions affect settling in magma chambers. Granular-scale models, using the lattice Boltzmann technique, have also permitted to study the migration of exsolved volatile bubbles in magma chambers at high crystal content (see Fig.…”

Numerical simulations of magmatic enclave deformation

“…As the flows simulated are in the laminar regime and the particle Reynolds numbers are also well below the transition to turbulence (Furuichi and Nishiura, 2014), the drag forces exerted by the fluid on the particles as well as gravity forces were calculated using an analytical simplification instead of the usual numerical evaluation (Garg et al, 2012). The reason behind this algorithmic modification can be understood by considering the equation of motion for the solids in the absence of particle contacts:…”

“…(1), which significantly decreases the computational costs. By capturing the particle acceleration curve, our approach builds on that used in Furuichi and Nishiura (2014), which assumes that particles systematically jump to their terminal velocities in one time step.…”

Modeling of Dynamic Rock–Fluid Interaction Using Coupled 3-D Discrete Element and Lattice Boltzmann Methods

“…Simulations that capture this interaction generally follow two approaches. The first approach incorporates fluid-solid interaction based on a locally averaged interaction between the two phases (Anderson and Jackson 1967;Tsuji et al 1993;Xu and Yu 1997;Tsuji et al 2008;Mikito and Daisuke 2014) while the second approach directly simulates hydrodynamic forces on the solid particles (Noble and Torczynski 1998;Holdych 2003;Owen et al 2010;Strack and Cook 2007). In the locally averaged approach, the fluid-solid coupling is performed by averaging the interactions over a representative volume and all particles within a local region experience the same hydrodynamic forces.…”