Title: Multiscale and equation-fee computing for lattice Boltzmann models
Other Titles: Meerschalige en vergelijkingsvrije simulaties met rooster Boltzmann modellen
Authors: Van Leemput, Pieter
Issue Date: 11-May-2007
Abstract: Due to a separation of time and space scales in their dynamics, many
physical and chemical systems can be described at different levels of
abstraction. We consider two multiscale modeling techniques that take
advantage of this scale separation: the equation-free framework
developed by Kevrekidis et al., which enables a time simulation for an
unknown macroscopic model using only microscopic or mesoscopic
simulations, and spatially hybrid models, which couple a
microscopic/mesoscopic particle-based method to a macroscopic continuum
model in space. At the microscopic/mesoscopic level, we consider
lattice Boltzmann models (LBMs) for one-dimensional reaction-diffusion
First, we show that time stepper based numerical bifurcation
analysis techniques developed for PDEs can be used for LBMs as
well. We use the LBM or the ``coarse'' equation-free time stepper
wrapped around the LBM as the time stepper.
Second, we focus on the multiscale interfacing problem. During
initialization and spatial coupling, one has to solve a one-to-many
problem. A few macroscopic quantities have to be mapped to meaningful
values for a larger set of microscopic/mesoscopic variables. We perform
an extensive study of the influence of the initialization process (also
called lifting or reconstruction) on the minimal time step of the
coarse time stepper and the accuracy of the results. Furthermore, we
analyze the behavior of the so-called constrained runs initialization
scheme for the LBMs considered. We prove that the scheme is
unconditionally stable and that it converges
to a first order
correct approximation of the Chapman-Enskog relations. We also
implement constrained runs schemes that use interpolation techniques to
obtain a higher order accuracy.
Finally, we analyze the spatial discretization error of the hybrid
model obtained by spatially coupling a LBM to a finite difference
discretization of a PDE and show that the global error of the hybrid
model is one order less accurate than the local error made at the
interface. At the interface, the Chapman-Enskog relations or the
constrained runs scheme can be used.
ISBN: 978-90-5682-806-6
Publication status: published
KU Leuven publication type: TH
Appears in Collections:Numerical Analysis and Applied Mathematics Section

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