A Hybrid Grid-Particle Method for Moving Bodies in 3D Stokes Flow with Variable Viscosity

Abstract

This article presents a new approach for the resolution of large three-dimensional Stokes equations with variable viscosity fluids, coupled with transport equations. After building the model, we will write these equations in the context of highly viscous flows and penalization, in order to consider complex geometries moving in a fluid. From a mathematical point of view, the solutions show nonlinear dynamics. Beside the use of standard tools such as finite differences and staggered grids, we have built a new methodology based on large three-dimensional simulations, including operators splitting for an efficient use of fast solvers, multi-index fixed point methods, Lagrangian methods with fast and accurate grid-particle transfers, and the multiresolution description of variables. Among the main original aspects of this method, both accurate incompressibility and variable viscosity are treated in the same fixed point. Hence the computation costs for variable and constant viscosity flows are similar. Several examples are given to validate the order of convergence and conservation rates. Such models are used, among other examples, in biological computing at the cellular scale. The present article eventually describes the ciliated epithelium cells covering a mammal's lungs, beating in a mucus film. This study of human lung diseases explores the efficiency of the mucociliary clearance, a challenging problem in health sciences, especially for the investigation of cystic fibrosis and various chronic obstructive pulmonary diseases.

On the effect of mucus rheology on the muco-ciliary transport

“…Using velocity transforms coefficient and changing the obtained velocity from Step 3 to physical velocity, the total force term ( f lb ) is obtained from Eq. (29). v. F α is computed from Eq.…”

“…They also represent that the windscreen wiper motion and rigid planar motion of cilia would decrease or almost stop the mucus transport. Chatelin and Poncet [29] modeled muco-ciliary clearance by using a hybrid scheme combining an Eulerian scheme for the Stokes equations and a particle method for transport equations. They [29] considered non-Newtonian aspects of viscosity in their method and study different mechanisms of mucus propelling and found dominant factors in muco-ciliary clearance, particularly in the context of cystic fibrosis and aerosol therapy.…”

“…Chatelin and Poncet [29] modeled muco-ciliary clearance by using a hybrid scheme combining an Eulerian scheme for the Stokes equations and a particle method for transport equations. They [29] considered non-Newtonian aspects of viscosity in their method and study different mechanisms of mucus propelling and found dominant factors in muco-ciliary clearance, particularly in the context of cystic fibrosis and aerosol therapy. Similar investigations were performed to study mucus flow using similar methods [30][31][32][33].…”

Upscaling Strategies of Porosity-Permeability Correlations in Reacting Environments from Pore-Scale Simulations

“…The more detailed ones solve the relevant flow equations or some approximation depending on the flow regime and the flow physics that are involved, in realistic geometries. Such methods are the lattice Boltzmann method [9][10][11][12][13], the methods based on particle hydrodynamics [14,15], as well as the standard finite volume methods when applied in complex geometries with moving boundaries [16][17][18]. Lattice Boltzmann models can resolve transport processes in realistic complex geometries, involving complex interactions between species and phases, but are more computational intensive compared to pore network models.…”

Numerical Investigation on Vortex Shedding from a Hydrofoil with a Beveled Trailing Edge

“…We employed the hybrid particle-mesh method and the vorticity-based subgrid scale model to undertake a numerical flow simulation. The hybrid particle-mesh method is a combination of the vortexin-cell (VIC) method (see [12][13][14][15] and references therein) and the penalization technique [16], which has been developed in recent years (see [17][18][19][20][21][22][23][24] for a review). The hybrid particle-mesh method enables the use of fast and efficient techniques for computing differential operators, thereby enabling large scale simulations.…”