Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method

The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule Freely Suspended in a Linear Shear Flow, J. Fluid Mech. 113 (1981) 251-267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak et al., Strain Energy Function of Red Blood Cell Membranes, Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy.Comment: 23 pages, 14 figures, 3 table

A conservative momentum exchange algorithm for interaction problem between fluid and deformable particles

This is the peer reviewed version of the following article:Shintaro Takeuchi, Yoshihiko Yuki, Atsushi Ueyama, Takeo Kajishima, "A conservative momentum exchange algorithm for interaction problem between fluid and deformable particles," International Journal for Numerical Methods in Fluids, Vol.64, Issue 10-12, pp.1084-1101, John Wiley & Sons, 2010, which has been published in final form at http://dx.doi.org/10.1002/fld.2272. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving

The motion of a deforming capsule through a corner

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A global spectral method is adopted to resolve the dynamics of the capsule membrane developing elastic tension according to the neo-Hookean constitutive law and bending moments in an inertialess flow. The simulations show that the trajectory of the capsule closely follows the underlying streamlines independently of the capillary number. The membrane deformability, on the other hand, significantly influences the relative area variations, the advection velocity and the principal tensions observed during the capsule motion. The evolution of the capsule velocity displays a loss of the time-reversal symmetry of Stokes flow due to the elasticity of the membrane. The velocity decreases while the capsule is approaching the corner as the background flow does, reaches a minimum at the corner and displays an overshoot past the corner due to the streamwise elongation induced by the flow acceleration in the downstream branch. This velocity overshoot increases with confinement while the maxima of the major principal tension increase linearly with the inverse of the duct width. Finally, the deformation and tension of the capsule are shown to decrease in a curved corner

A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with ad- hoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors

Progress in particle-based multiscale and hybrid methods for flow applications

This work focuses on the review of particle-based multiscale and hybrid methods that have surfaced in the field of fluid mechanics over the last 20 years. We consider five established particle methods: molecular dynamics, direct simulation Monte Carlo, lattice Boltzmann method, dissipative particle dynamics and smoothed-particle hydrodynamics. A general description is given on each particle method in conjunction with multiscale and hybrid applications. An analysis on the length scale separation revealed that current multiscale methods only bridge across scales which are of the order of O(102)−O(103) and that further work on complex geometries and parallel code optimisation is needed to increase the separation. Similarities between methods are highlighted and combinations discussed. Advantages, disadvantages and applications of each particle method have been tabulated as a reference

Red Blood Cell Dynamics on Non-Uniform Grids using a Lattice Boltzmann Flux Solver and a Spring-Particle Red Blood Cell Model

The Computational Haemodynamics Research Group (CHRG) in Technological University Dublin is developing a computational fluid dynamics (CFD) software package aimed specifically at physiologically-realistic modelling of blood flow. A physiologically-realistic model of blood flow involves calculating the deformation of individual red blood cells (RBCs) and the contribution of this deformation to the overall blood flow. The CHRG has developed an enhanced spring-particle RBC structural model that is capable of modelling the full stomatocyte-discocyteechinocyte (SDE) transformation. This RBC model, incorporated into a fluid dynamics solver, will provide a physiologically-realistic blood flow model. In this work the overall plasma flow is modelled using a novel technique: the lattice Boltzmann flux solver (LBFS). This is an innovative approach to solving the NavierStokes (N-S) equations for fluid flow. It involves solving the macroscopic equations using the finite volume method (FVM) and calculating the flux across the cell interfaces via a local reconstruction of the lattice Boltzmann equation (LBE). Fluidstruture interaction between the RBC and the plasma is captured by coupling the RBC solver to the LBFS via the immersed boundary method (IBM). Numerical experiments investigating RBC dynamics are performed using non-uniform grids and validated against existing experimental data in the literature. Finally all numerical solvers are developed using general purpose GPU programming (GPGPU) and this is shown to accelerate simulation runtimes significantly