56 research outputs found
Towards learning Lattice Boltzmann collision operators
In this work we explore the possibility of learning from data collision
operators for the Lattice Boltzmann Method using a deep learning approach. We
compare a hierarchy of designs of the neural network (NN) collision operator
and evaluate the performance of the resulting LBM method in reproducing time
dynamics of several canonical flows. In the current study, as a first attempt
to address the learning problem, the data was generated by a single relaxation
time BGK operator. We demonstrate that vanilla NN architecture has very limited
accuracy. On the other hand, by embedding physical properties, such as
conservation laws and symmetries, it is possible to dramatically increase the
accuracy by several orders of magnitude and correctly reproduce the short and
long time dynamics of standard fluid flows
Modeling anisotropic diffusion using a departure from isotropy approach
There are a large number of finite volume solvers available for solution of isotropic diffusion equation. This article presents an approach of adapting these solvers to solve anisotropic diffusion equations. The formulation works by decomposing the diffusive flux into a component associated with isotropic diffusion and another component associated with departure from isotropic diffusion. This results in an isotropic diffusion equation with additional terms to account for the anisotropic effect. These additional terms are treated using a deferred correction approach and coupled via an iterative procedure. The presented approach is validated against various diffusion problems in anisotropic media with known analytical or numerical solutions. Although demonstrated for two-dimensional problems, extension of the present approach to three-dimensional problems is straight forward. Other than the finite volume method, this approach can be applied to any discretization method
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Dispersion reducing methods for edge discretizations of the electric vector wave equation
We present a novel strategy for minimizing the numerical dispersion error in edge discretizations of the time-domain electric vector wave equation on square meshes based on the mimetic finite difference (MFD) method. We compare this strategy, called M-adaptation, to two other discretizations, also based on square meshes. One is the lowest order Nédélec edge element discretization. The other is a modified quadrature approach (GY-adaptation) proposed by Guddati and Yue for the acoustic wave equation in two dimensions. All three discrete methods use the same edge-based degrees of freedom, while the temporal discretization is performed using the standard explicit Leapfrog scheme. To obtain efficient and explicit time stepping methods, the three schemes are further mass lumped. We perform a dispersion and stability analysis for the presented schemes and compare all three methods in terms of their stability regions and phase error. Our results indicate that the method produced by GY-adaptation and the Nédélec method are both second order accurate for numerical dispersion, but differ in the order of their numerical anisotropy (fourth order, versus second order, respectively). The result of M-adaptation is a discretization that is fourth order accurate for numerical dispersion as well as numerical anisotropy. Numerical simulations are provided that illustrate the theoretical results.Keywords: Nédélec edge elements, Vector wave equation, M-adaptation, Maxwell’s equations, Anisotropy, Dispersio
Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering
Bacterial processes ranging from gene expression to motility and biofilm
formation are constantly challenged by internal and external noise. While the
importance of stochastic fluctuations has been appreciated for chemotaxis, it
is currently believed that deterministic long-range fluid dynamical effects
govern cell-cell and cell-surface scattering - the elementary events that lead
to swarming and collective swimming in active suspensions and to the formation
of biofilms. Here, we report the first direct measurements of the bacterial
flow field generated by individual swimming Escherichia coli both far from and
near to a solid surface. These experiments allowed us to examine the relative
importance of fluid dynamics and rotational diffusion for bacteria. For
cell-cell interactions it is shown that thermal and intrinsic stochasticity
drown the effects of long-range fluid dynamics, implying that physical
interactions between bacteria are determined by steric collisions and
near-field lubrication forces. This dominance of short-range forces closely
links collective motion in bacterial suspensions to self-organization in driven
granular systems, assemblages of biofilaments, and animal flocks. For the
scattering of bacteria with surfaces, long-range fluid dynamical interactions
are also shown to be negligible before collisions; however, once the bacterium
swims along the surface within a few microns after an aligning collision,
hydrodynamic effects can contribute to the experimentally observed, long
residence times. As these results are based on purely mechanical properties,
they apply to a wide range of microorganisms.Comment: 9 pages, 2 figures, http://www.pnas.org/content/108/27/1094
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