166 research outputs found
Coarse Bifurcation Studies of Bubble Flow Microscopic Simulations
The parametric behavior of regular periodic arrays of rising bubbles is
investigated with the aid of 2-dimensional BGK Lattice-Boltzmann (LB)
simulators. The Recursive Projection Method is implemented and coupled to the
LB simulators, accelerating their convergence towards what we term coarse
steady states. Efficient stability/bifurcation analysis is performed by
computing the leading eigenvalues/eigenvectors of the coarse time stepper. Our
approach constitutes the basis for system-level analysis of processes modeled
through microscopic simulations.Comment: 4 pages, 3 figure
A simplified particulate model for coarse-grained hemodynamics simulations
Human blood flow is a multi-scale problem: in first approximation, blood is a
dense suspension of plasma and deformable red cells. Physiological vessel
diameters range from about one to thousands of cell radii. Current
computational models either involve a homogeneous fluid and cannot track
particulate effects or describe a relatively small number of cells with high
resolution, but are incapable to reach relevant time and length scales. Our
approach is to simplify much further than existing particulate models. We
combine well established methods from other areas of physics in order to find
the essential ingredients for a minimalist description that still recovers
hemorheology. These ingredients are a lattice Boltzmann method describing rigid
particle suspensions to account for hydrodynamic long range interactions
and---in order to describe the more complex short-range behavior of
cells---anisotropic model potentials known from molecular dynamics simulations.
Paying detailedness, we achieve an efficient and scalable implementation which
is crucial for our ultimate goal: establishing a link between the collective
behavior of millions of cells and the macroscopic properties of blood in
realistic flow situations. In this paper we present our model and demonstrate
its applicability to conditions typical for the microvasculature.Comment: 12 pages, 11 figure
Coarse-grained numerical bifurcation analysis of lattice Boltzmann models
In this paper we study the earlier proposed coarse-grained bifurcation analysis approach. We extend the results obtained then for a one-dimensional FitzHugh–Nagumo lattice Boltzmann (LB) model in several ways. First, we extend the coarse-grained time stepper concept to enable the computation of periodic solutions and we use the more versatile Newton–Picard method rather than the Recursive Projection Method (RPM) for the numerical bifurcation analysis. Second, we compare the obtained bifurcation diagram with the bifurcation diagrams of the corresponding macroscopic PDE and of the lattice Boltzmann model. Most importantly, we perform an extensive study of the influence of the lifting or reconstruction step on the minimal successful time step of the coarse-grained time stepper and the accuracy of the results. It is shown experimentally that this time step must often be much larger than the time it takes for the higher-order moments to become slaved by the lowest-order moment, which somewhat contradicts earlier claims.
Investigation of haemodynamic markers for stenosis development
Abstract Different hemodynamic markers for stenosis development are considered, assessed and compared. A recently proposed numerical approach is employed, where stenosis development is modeled based on the local hemodynamic conditions at the artery wall, determined using the lattice Boltzmann method. A range of hemodynamic markers, commonly associated in the literature with the progression of atherosclerosis, were considered. It was observed that using the oscillatory shear index, which is related to the wall shear stress oscillating from its mean direction, did not produce a realistic stenosis development. The other markers produced stenosis growth comparable with observations from the literature
Simulation of Cavity Flow by the Lattice Boltzmann Method
A detailed analysis is presented to demonstrate the capabilities of the
lattice Boltzmann method. Thorough comparisons with other numerical solutions
for the two-dimensional, driven cavity flow show that the lattice Boltzmann
method gives accurate results over a wide range of Reynolds numbers. Studies of
errors and convergence rates are carried out. Compressibility effects are
quantified for different maximum velocities, and parameter ranges are found for
stable simulations. The paper's objective is to stimulate further work using
this relatively new approach for applied engineering problems in transport
phenomena utilizing parallel computers.Comment: Submitted to J. Comput. Physics, late
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