2,287 research outputs found
Multiscale lattice Boltzmann approach to modeling gas flows
For multiscale gas flows, kinetic-continuum hybrid method is usually used to
balance the computational accuracy and efficiency. However, the
kinetic-continuum coupling is not straightforward since the coupled methods are
based on different theoretical frameworks. In particular, it is not easy to
recover the non-equilibrium information required by the kinetic method which is
lost by the continuum model at the coupling interface. Therefore, we present a
multiscale lattice Boltzmann (LB) method which deploys high-order LB models in
highly rarefied flow regions and low-order ones in less rarefied regions. Since
this multiscale approach is based on the same theoretical framework, the
coupling precess becomes simple. The non-equilibrium information will not be
lost at the interface as low-order LB models can also retain this information.
The simulation results confirm that the present method can achieve model
accuracy with reduced computational cost
A Hierarchy of Hybrid Numerical Methods for Multi-Scale Kinetic Equations
In this paper, we construct a hierarchy of hybrid numerical methods for
multi-scale kinetic equations based on moment realizability matrices, a concept
introduced by Levermore, Morokoff and Nadiga. Following such a criterion, one
can consider hybrid scheme where the hydrodynamic part is given either by the
compressible Euler or Navier-Stokes equations, or even with more general
models, such as the Burnett or super-Burnett systems.Comment: 27 pages, edit: typo and metadata chang
Adaptive multiscale methods for 3D streamer discharges in air
We discuss spatially and temporally adaptive implicit-explicit (IMEX) methods
for parallel simulations of three-dimensional fluid streamer discharges in
atmospheric air. We examine strategies for advancing the fluid equations and
elliptic transport equations (e.g. Poisson) with different time steps,
synchronizing them on a global physical time scale which is taken to be
proportional to the dielectric relaxation time. The use of a longer time step
for the electric field leads to numerical errors that can be diagnosed, and we
quantify the conditions where this simplification is valid. Likewise, using a
three-term Helmholtz model for radiative transport, the same error diagnostics
show that the radiative transport equations do not need to be resolved on time
scales finer than the dielectric relaxation time. Elliptic equations are
bottlenecks for most streamer simulation codes, and the results presented here
potentially provide computational savings. Finally, a computational example of
3D branching streamers in a needle-plane geometry that uses up to 700 million
grid cells is presented.Comment: 17 pages, 5 figure
Reduction of dynamical biochemical reaction networks in computational biology
Biochemical networks are used in computational biology, to model the static
and dynamical details of systems involved in cell signaling, metabolism, and
regulation of gene expression. Parametric and structural uncertainty, as well
as combinatorial explosion are strong obstacles against analyzing the dynamics
of large models of this type. Multi-scaleness is another property of these
networks, that can be used to get past some of these obstacles. Networks with
many well separated time scales, can be reduced to simpler networks, in a way
that depends only on the orders of magnitude and not on the exact values of the
kinetic parameters. The main idea used for such robust simplifications of
networks is the concept of dominance among model elements, allowing
hierarchical organization of these elements according to their effects on the
network dynamics. This concept finds a natural formulation in tropical
geometry. We revisit, in the light of these new ideas, the main approaches to
model reduction of reaction networks, such as quasi-steady state and
quasi-equilibrium approximations, and provide practical recipes for model
reduction of linear and nonlinear networks. We also discuss the application of
model reduction to backward pruning machine learning techniques
Multiphysics simulations of collisionless plasmas
Collisionless plasmas, mostly present in astrophysical and space
environments, often require a kinetic treatment as given by the Vlasov
equation. Unfortunately, the six-dimensional Vlasov equation can only be solved
on very small parts of the considered spatial domain. However, in some cases,
e.g. magnetic reconnection, it is sufficient to solve the Vlasov equation in a
localized domain and solve the remaining domain by appropriate fluid models. In
this paper, we describe a hierarchical treatment of collisionless plasmas in
the following way. On the finest level of description, the Vlasov equation is
solved both for ions and electrons. The next courser description treats
electrons with a 10-moment fluid model incorporating a simplified treatment of
Landau damping. At the boundary between the electron kinetic and fluid region,
the central question is how the fluid moments influence the electron
distribution function. On the next coarser level of description the ions are
treated by an 10-moment fluid model as well. It may turn out that in some
spatial regions far away from the reconnection zone the temperature tensor in
the 10-moment description is nearly isotopic. In this case it is even possible
to switch to a 5-moment description. This change can be done separately for
ions and electrons. To test this multiphysics approach, we apply this full
physics-adaptive simulations to the Geospace Environmental Modeling (GEM)
challenge of magnetic reconnection.Comment: 13 pages, 5 figure
The Moment Guided Monte Carlo method for the Boltzmann equation
In this work we propose a generalization of the Moment Guided Monte Carlo
method developed in [11]. This approach permits to reduce the variance of the
particle methods through a matching with a set of suitable macroscopic moment
equations. In order to guarantee that the moment equations provide the correct
solutions, they are coupled to the kinetic equation through a non equilibrium
term. Here, at the contrary to the previous work in which we considered the
simplified BGK operator, we deal with the full Boltzmann operator. Moreover, we
introduce an hybrid setting which permits to entirely remove the resolution of
the kinetic equation in the limit of infinite number of collisions and to
consider only the solution of the compressible Euler equation. This
modification additionally reduce the statistical error with respect to our
previous work and permits to perform simulations of non equilibrium gases using
only a few number of particles. We show at the end of the paper several
numerical tests which prove the efficiency and the low level of numerical noise
of the method.Comment: arXiv admin note: text overlap with arXiv:0908.026
Error analysis of coarse-grained kinetic Monte Carlo method
In this paper we investigate the approximation properties of the
coarse-graining procedure applied to kinetic Monte Carlo simulations of lattice
stochastic dynamics. We provide both analytical and numerical evidence that the
hierarchy of the coarse models is built in a systematic way that allows for
error control in both transient and long-time simulations. We demonstrate that
the numerical accuracy of the CGMC algorithm as an approximation of stochastic
lattice spin flip dynamics is of order two in terms of the coarse-graining
ratio and that the natural small parameter is the coarse-graining ratio over
the range of particle/particle interactions. The error estimate is shown to
hold in the weak convergence sense. We employ the derived analytical results to
guide CGMC algorithms and we demonstrate a CPU speed-up in demanding
computational regimes that involve nucleation, phase transitions and
metastability.Comment: 30 page
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