Elsevier

Journal of Computational Physics

Volume 256, 1 January 2014, Pages 465-483
Journal of Computational Physics

An unstructured solver for simulations of deformable particles in flows at arbitrary Reynolds numbers

https://doi.org/10.1016/j.jcp.2013.08.061Get rights and content

Highlights

  • We model deformable particles under flows at arbitrary Reynolds numbers.

  • The immersed boundary method is adapted to an unstructured finite-volume solver.

  • A specific algorithm is introduced to ensure volume conservation of particles.

  • Reference 2-D test cases are reported to enable quantitative validation in 2-D.

  • The method is robust in a configuration typical of industrial cytometers.

Abstract

As a step in the development of a numerical procedure able to perform parallel computations of the dynamics of capsules/cells in non-physiological configurations, a numerical method is developed and its validation is described. The fluid–structure interaction problem is solved using an immersed boundary method, adapted to an unstructured finite-volume flow solver thanks to the reproducing kernel particle method. A specific treatment to ensure volume conservation of the fluid enclosed in the immersed structure is also detailed. The present paper focuses on quantitative validation of the method in 2-D, against existing reference 2-D results. Excellent agreement is obtained for configurations of capsules and vesicles evolving with or without mean flow. Applications of the method to non-zero-Reynolds-number cases, including non-trivial geometry, is shown. This unstructured immersed boundary method proves robust to tackle the dynamics of deformable particles in complex flows.

Section snippets

Motivation and objectives

Over the last decades, numerical simulation of capsules, vesicles and cells under flow has developed tremendously. All these systems, which will be referred to as deformable particles, are constituted by a liquid droplet enclosed by a very thin structure (its thickness is much smaller than the size of the object). This structure can be a polymer structure for capsules, a phospholipid bilayer for vesicles or a more complex biological membrane in the case of red blood cells [1]. Computing the

Modeling framework

The present numerical method is dedicated to the numerical simulation of the dynamics of deformable particles, composed by an internal fluid enclosed by a flexible structure. The fluid inside and outside the cell is supposed to be incompressible and Newtonian. The fluid flow is thus governed by the incompressible versions of the continuity and the Navier–Stokes equations:.u=0,ρ(ut+u.u)=p+.[μ(u+(u)T)], where u is the fluid velocity, p the pressure and t the time. The dynamic viscosity μ

Validations

This section is dedicated to the validation of the FSI solver, named YALES2BIO. As the present numerical method is not standard, validation is very detailed to prove the quality of the results. Validation notably involves test cases related to vesicles (i.e. particles with strong resistance to stretching and bending resistance) and capsules (i.e. particles with elastic membranes without bending resistance).

Applications

The study of microcirculation is one of the primary objectives for developing numerical methods based on boundary integrals. Indeed, the use of relatively simple geometries and the zero-Reynolds-number assumption are not restrictive in that context. The Reynolds number in capillaries is indeed of order of 103. In addition, in the circulatory system, the shear stress seen by red blood cells remains moderate (except in some specific cases as severe stenoses [74]) so that the particle Reynolds

Conclusion

A numerical method for simulations of the dynamics of deformable objects constituted by a liquid droplet enclosed in a flexible structure is presented. The approach is based on the immersed boundary method adapted to unstructured grids with the reproducing kernel particle method. The specificity of the method is to enable calculations at high Reynolds number, in complex geometries using body-fitted unstructured grids. The unstructured IBM is supplemented with a volume-conservation algorithm

Acknowledgements

The authors acknowledge support from ANR, through the project FORCE (Flows Of Red blood CElls), in which the YALES2BIO solver has been developed. The authors also acknowledge the support of OSEO, via the DAT@DIAG project. Vincent Moureau, Vanessa Lleras and Marco Martins Afonso are thanked for helpful discussions. The authors also thank the NUMEV Labex for support.

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