Spatial Coupling of a Lattice Boltzmann fluid model with a Finite Difference Navier-Stokes solver

In multiscale, multi-physics applications, there is an increasing need for coupling numerical solvers that are each applied to a different part of the problem. Here we consider the case of coupling a Lattice Boltzmann fluid model and a Finite Difference Navier-Stokes solver. The coupling is implemented so that the entire computational domain can be divided in two regions, with the FD solver running on one of them and the LB one on the other. We show how the various physical quantities of the two approaches should be related to ensure a smooth transition at the interface between the regions. We demonstrate the feasibility of the method on the Poiseuille flow, where the LB and FD schemes are used on adjacent sub-domains. The same idea can be also developed to couple LB models with Finite Volumes, or Finite Elements calculations. The motivation for developing such a type of coupling is that, depending on the geometry of the flow, one technique can be more efficient, less memory consuming, or physically more appropriate than the other in some regions (e.g. near the boundaries), whereas the converse is true for other parts of the same system. We can also imagine that a given system solved, say by FD, can be augmented in some spatial regions with a new physical process that is better treated by a LB model. Our approach allows us to only modify the concerned region without altering the rest of the computation.Comment: 10 pages, 2 figure

Bridging the computational gap between mesoscopic and continuum modeling of red blood cells for fully resolved blood flow

We present a computational framework for the simulation of blood flow with fully resolved red blood cells (RBCs) using a modular approach that consists of a lattice Boltzmann solver for the blood plasma, a novel finite element based solver for the deformable bodies and an immersed boundary method for the fluid-solid interaction. For the RBCs, we propose a nodal projective FEM (npFEM) solver which has theoretical advantages over the more commonly used mass-spring systems (mesoscopic modeling), such as an unconditional stability, versatile material expressivity, and one set of parameters to fully describe the behavior of the body at any mesh resolution. At the same time, the method is substantially faster than other FEM solvers proposed in this field, and has an efficiency that is comparable to the one of mesoscopic models. At its core, the solver uses specially defined potential energies, and builds upon them a fast iterative procedure based on quasi-Newton techniques. For a known material, our solver has only one free parameter that demands tuning, related to the body viscoelasticity. In contrast, state-of-the-art solvers for deformable bodies have more free parameters, and the calibration of the models demands special assumptions regarding the mesh topology, which restrict their generality and mesh independence. We propose as well a modification to the potential energy proposed by Skalak et al. 1973 for the red blood cell membrane, which enhances the strain hardening behavior at higher deformations. Our viscoelastic model for the red blood cell, while simple enough and applicable to any kind of solver as a post-convergence step, can capture accurately the characteristic recovery time and tank-treading frequencies. The framework is validated using experimental data, and it proves to be scalable for multiple deformable bodies

Competing Species Dynamics: Qualitative Advantage versus Geography

A simple cellular automata model for a two-group war over the same territory is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are instrumental to overcome a less fitted majority. The model applies to a large spectrum of competing groups: smoker-non smoker war, epidemic spreading, opinion formation, competition for industrial standards and species evolution. In the last case, it provides a new explanation for punctuated equilibria.Comment: 7 pages, latex, 2 figures include

Lattice Boltzmann Simulations of Blood Flow: Non-Newtonian Rheology and Clotting Processes

The numerical simulation of thrombosis in stented aneurysms is an important issue to estimate the efficiency of a stent. In this paper, we consider a Lattice Boltzmann (LB) approach to bloodflow modeling and we implement a non-Newtonian correction in order to reproduce more realistic flow profiles. We obtain a good agreement between simulations and Casson's model of blood rheology in a simple geometry. Finally we discuss how, by using a passive scalar suspension model with aggregation on top of the LB dynamics, we can describe the clotting processes in the aneurys

Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics

The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expansion in Hermite polynomials, that greatly improves the accuracy and stability of the LBM without altering significantly its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between our approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial softwares, while here the entire theoretical framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of America (in press

Lattice Boltzmann Solid Particles in a Lattice Boltzmann Fluid

We define a lattice Boltzmann model of solid, deformable suspensions immersed in a fluid itself described in terms of the lattice Boltzmann method. We discuss the rules governing the internal dynamics of the solid object as well as the rules specifying the interaction between solid and fluid particle. We perform a numerical drag experiment to validate the model. Finally we consider the case of a population of flexible chains in suspension in a shear stress flow and study the influence on the velocity profil