An unstructured solver for simulations of deformable particles in flows at arbitrary Reynolds numbers
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: 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 . 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.
References (76)
Capsule motion in flow: Deformation and membrane buckling
C. R. Phys.
(2009)Modeling the motion of capsules in flow
Curr. Opin. Colloid Interface Sci.
(2011)- et al.
A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D
J. Comput. Phys.
(2009) - et al.
3D vesicle dynamics simulations with a linearly triangulated surface
J. Comput. Phys.
(2011) - et al.
A spectral boundary integral method for flowing blood cells
J. Comput. Phys.
(2010) - et al.
A multiscale red blood cell model with accurate mechanics, rheology, and dynamics
Biophys. J.
(2010) - et al.
Deformation of elastic particles in viscous shear flow
J. Comput. Phys.
(2009) - et al.
Applications of level set methods in computational biophysics
Math. Comput. Model.
(2009) - et al.
A level set projection model of lipid vesicles in general flows
J. Comput. Phys.
(2011) - et al.
Extended immersed boundary method using FEM and RKPM
Comput. Methods Appl. Mech. Eng.
(2004)
Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method
J. Comput. Phys.
An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries
J. Comput. Phys.
Large deformation of liquid capsules enclosed by thin shells immersed in the fluid
J. Comput. Phys.
The use of computational fluid dynamics in the development of ventricular assist devices
Med. Eng. Phys.
Immersed finite element method
Comput. Methods Appl. Mech. Eng.
Rheology of red blood cell aggregation by computer simulation
J. Comput. Phys.
Numerical analysis of blood flow in the heart
J. Comput. Phys.
An adaptive version of the immersed boundary method
J. Comput. Phys.
A front-tracking method for viscous, incompressible, multi-fluid flows
J. Comput. Phys.
Design of a massively parallel CFD code for complex geometries
C. R., Méc.
From large-eddy simulation to direct numerical simulation of a lean premixed swirl flame: Filtered laminar flame-PDF modelling
Comput. Fluids
Immersed-boundary methods for general finite-difference and finite-volume Navier–Stokes solvers
J. Comput. Phys.
An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane
J. Comput. Phys.
Vesicles, capsules and red blood cells under flow
J. Phys. Conf. Ser.
Modeling and Simulation of Capsules and Biological Cells
Computational Hydrodynamics of Capsules and Biological Cells
Boundary Integral and Singularity Methods for Linearized Viscous Flow
Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities
J. Fluid Mech.
Hydrodynamic interaction between two identical capsules in simple shear flow
J. Fluid Mech.
Dynamics of strain-hardening and strain-softening capsules in strong planar extensional flows via an interfacial spectral boundary element algorithm for elastic membranes
J. Fluid Mech.
Coupling of finite element and boundary integral methods for a capsule in a Stokes flow
Int. J. Numer. Methods Eng.
Motion of a two-dimensional elastic capsule in a branching channel flow
J. Fluid Mech.
Rheology of a dilute two-dimensional suspension of vesicles
J. Fluid Mech.
Three-dimensional vesicles under shear flow: Numerical study of dynamics and phase diagram
Phys. Rev. E
The dynamics of a vesicle in simple shear flow
J. Fluid Mech.
Numerical simulation of the flow-induced deformation of red blood cells
Ann. Biomed. Eng.
Multiscale modelling of erythrocytes in Stokes flow
J. Fluid Mech.
Swinging and tumbling of fluid vesicles in shear flow
Phys. Rev. Lett.
Cited by (47)
A Cartesian-octree adaptive front-tracking solver for immersed biological capsules in large complex domains
2023, Journal of Computational PhysicsAn isogeometric boundary element method for soft particles flowing in microfluidic channels
2021, Computers and FluidsCitation Excerpt :There are a variety of different computational strategies to solve FSI problems. Recently developed approaches can be broadly classified into three categories (see, e.g., the reviews [11] for capsules, [15] for vesicles, and [12] for RBCs), namely bulk mesh-based methods [16–19], particle-based methods [20–22], and boundary-element methods (BEMs). The BEM offers very high accuracy compared to other methods in the prediction of the dynamics of deformable particles immersed in inertialess Newtonian flows.
The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics
2021, Journal of Computational PhysicsCitation Excerpt :Although this issue was first mentioned more than two decades ago [15], solving this problem at its root and without side effects that limit the applicability of the resulting immersed method has proven to be extremely challenging. In the case of discretizations based on finite differences or finite volumes, the dominant error is due to the fact that the Lagrangian velocity obtained from the Eulerian velocity using discretized delta functions is far from being a solenoidal field even if the Eulerian velocity is properly enforced to be divergence-free with respect to the finite-difference/finite-volume approximation of the divergence operator [15,20,21]. In the case of discretizations based on finite elements, the dominant error is due to the fact that the weakly divergence-free Eulerian velocity is far from being a solenoidal field [22,23,18].
The rheology of soft bodies suspended in the simple shear flow of a viscoelastic fluid
2019, Journal of Non-Newtonian Fluid MechanicsCitation Excerpt :In Newtonian fluids immersed finite element methods have been implemented for solid particles with finite elasticity [54,55]. Additionally, a host of immersed boundary and boundary element methods have been utilized for capsules (infinitely thin sacks with fluid inside and outside) [3,10,25,26,30,32,36,44]. In viscoelastic fluids, methods including immersed boundary methods for capsules have been developed but no extensions to soft solid bodies have been presented [33,34].
An immersed boundary method for incompressible flows in complex domains
2019, Journal of Computational PhysicsCitation Excerpt :Pinelli et al. [5] adopted Reproducing Kernel Particle Methods (RKPM) [41] to redistribute the interpolation/spreading weights so that they satisfy the moment conditions and force conservation when the discrete delta functions are applied to curvilinear meshes. This has been successfully applied to an unstructured mesh framework [42]. Based on the recent developments in the literature discussed above, there is a need to further improve the formulation and the implementation of the IBM in order for the method to be relevant for many types of applications and more general numerical frameworks.
Shape dynamics of capsules in two phase-shifted orthogonal ultrasonic standing waves: A numerical investigation
2023, Journal of Fluid Mechanics