4,452 research outputs found
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
Hydro-micromechanical modeling of wave propagation in saturated granular media
Biot's theory predicts the wave velocities of a saturated poroelastic
granular medium from the elastic properties, density and geometry of its dry
solid matrix and the pore fluid, neglecting the interaction between constituent
particles and local flow. However, when the frequencies become high and the
wavelengths comparable with particle size, the details of the microstructure
start to play an important role. Here, a novel hydro-micromechanical numerical
model is proposed by coupling the lattice Boltzmann method (LBM) with the
discrete element method (DEM. The model allows to investigate the details of
the particle-fluid interaction during propagation of elastic waves While the
DEM is tracking the translational and rotational motion of each solid particle,
the LBM can resolve the pore-scale hydrodynamics. Solid and fluid phases are
two-way coupled through momentum exchange. The coupling scheme is benchmarked
with the terminal velocity of a single sphere settling in a fluid. To mimic a
pressure wave entering a saturated granular medium, an oscillating pressure
boundary condition on the fluid is implemented and benchmarked with
one-dimensional wave equations. Using a face centered cubic structure, the
effects of input waveforms and frequencies on the dispersion relations are
investigated. Finally, the wave velocities at various effective confining
pressures predicted by the numerical model are compared with with Biot's
analytical solution, and a very good agreement is found. In addition to the
pressure and shear waves, slow compressional waves are observed in the
simulations, as predicted by Biot's theory.Comment: Manuscript submitted to International Journal for Numerical and
Analytical Methods in Geomechanic
Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation
Micro–macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro–macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation by a lattice-Boltzmann one. The kinetic model is given by molecular analogy with a finitely extensible non-linear elastic (FENE) dumbbell and is deterministically solved through an equivalent Fokker–Planck equation. The key features of the proposed approach are: (i) a proper scaling and coupling between the micro lattice-Boltzmann solution and the macro finite-volume one; (ii) a fast microscopic solver thanks to an implementation for Graphic Processing Unit (GPU) and the local adaptivity of the lattice-Boltzmann mesh; (iii) an operator-splitting algorithm for the convection of the macroscopic viscoelastic stresses instead of the whole probability density of the dumbbell configuration. This latter feature allows the application of the proposed method to non-homogeneous flow conditions with low memory-storage requirements. The model optimization is achieved through an extensive analysis of the lattice-Boltzmann solution, which finally provides control on the numerical error and on the computational time. The resulting micro–macro model is validated against the benchmark problem of a viscoelastic flow past a confined cylinder and the results obtained confirm the validity of the approach
Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations
A numerical method, based on the discrete lattice Boltzmann equation, is
presented for solving the volume-averaged Navier-Stokes equations. With a
modified equilibrium distribution and an additional forcing term, the
volume-averaged Navier-Stokes equations can be recovered from the lattice
Boltzmann equation in the limit of small Mach number by the Chapman-Enskog
analysis and Taylor expansion. Due to its advantages such as explicit solver
and inherent parallelism, the method appears to be more competitive with
traditional numerical techniques. Numerical simulations show that the proposed
model can accurately reproduce both the linear and nonlinear drag effects of
porosity in the fluid flow through porous media.Comment: 9 pages, 2 figure
Detailed analysis of the lattice Boltzmann method on unstructured grids
The lattice Boltzmann method has become a standard for efficiently solving
problems in fluid dynamics. While unstructured grids allow for a more efficient
geometrical representation of complex boundaries, the lattice Boltzmann methods
is often implemented using regular grids. Here we analyze two implementations
of the lattice Boltzmann method on unstructured grids, the standard forward
Euler method and the operator splitting method. We derive the evolution of the
macroscopic variables by means of the Chapman-Enskog expansion, and we prove
that it yields the Navier-Stokes equation and is first order accurate in terms
of the temporal discretization and second order in terms of the spatial
discretization. Relations between the kinetic viscosity and the integration
time step are derived for both the Euler method and the operator splitting
method. Finally we suggest an improved version of the bounce-back boundary
condition. We test our implementations in both standard benchmark geometries
and in the pore network of a real sample of a porous rock.Comment: 42 page
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