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Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2013

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

Résumé

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.
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Dates et versions

hal-02010645 , version 1 (07-02-2019)

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Robin Chatelin, Philippe Poncet. A Hybrid Grid-Particle Method for Moving Bodies in 3D Stokes Flow with Variable Viscosity. SIAM Journal on Scientific Computing, 2013, 35 (4), pp.B925-B949. ⟨10.1137/120892921⟩. ⟨hal-02010645⟩
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