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Lattice Boltzmann in micro- and nano- flow simulations
This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.One of the fundamental difficulties in micro- and nano-flow simulations is that the
validity’s of the continuum assumption and the hydro-dynamic equations start to become questionable in this flow regime. The lower-level kinetic/molecular alternatives are often either prohibitively expensive for practical purposes or poorly justified from a fundamental perspective. The lattice
Boltzmann (LB) method, which originated from a simplistic Boolean kinetic model, is recently shown to converge asymptotically to the continuum Boltzmann-BGK equation and therefore offers a theoretically sound and computationally effective approach for micro- and nano-flow simulations. In addition, its kinetic nature allows certain microscopic physics to be modeled at the macroscopic level, leading to a highly efficient model for multiphase flows with phase transitions. With the inherent computational advantages of a lattice model, e.g., the algorithm simplicity and parallelizability, the
ease of handling complex geometry and so on, the LB method has found many applications in various areas of Computational Fluid Dynamics (CFD) and matured to the extend of commercial applications. In this talk, I shall give an introduction to the LB method with the emphasis given to the theoretical
justifications for its applications in micro- and nano-flow simulations. Some recent examples will also be reported
A fully relativistic lattice Boltzmann algorithm
Starting from the Maxwell-Juettner equilibrium distribution, we develop a
relativistic lattice Boltzmann (LB) algorithm capable of handling
ultrarelativistic systems with flat, but expanding, spacetimes. The algorithm
is validated through simulations of quark-gluon plasma, yielding excellent
agreement with hydrodynamic simulations. The present scheme opens the
possibility of transferring the recognized computational advantages of lattice
kinetic theory to the context of both weakly and ultra-relativistic systems.Comment: 12 pages, 8 figure
Fluid-Structure Interaction Simulation of a Coriolis Mass Flowmeter using a Lattice Boltzmann Method
In this paper we use a fluid-structure interaction (FSI) approach to simulate
a Coriolis mass flowmeter (CMF). The fluid dynamics are calculated by the open
source framework OpenLB, based on the lattice Boltzmann method (LBM). For the
structural dynamics we employ the open source software Elmer, an implementation
of the finite element method (FEM). A staggered coupling approach between the
two software packages is presented. The finite element mesh is created by the
mesh generator Gmsh to ensure a complete open source workflow. The Eigenmodes
of the CMF, which are calculated by modal analysis are compared with
measurement data. Using the estimated excitation frequency, a fully coupled,
partitioned, FSI simulation is applied to simulate the phase shift of the
investigated CMF design. The calculated phaseshift values are in good agreement
to the measurement data and verify the suitability of the model to numerically
describe the working principle of a CMF
Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic
fluids recently proposed in Ref. [1], is presented. The method is numerically
validated and applied to the case of two quite different relativistic fluid
dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the
impact of a supernova blast-wave on massive interstellar clouds. Close to
second order convergence with the grid resolution, as well as linear dependence
of computational time on the number of grid points and time-steps, are
reported
Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions
The complexity of the interactions between the constituent granular and
liquid phases of a suspension requires an adequate treatment of the
constituents themselves. A promising way for numerical simulations of such
systems is given by hybrid computational frameworks. This is naturally done,
when the Lagrangian description of particle dynamics of the granular phase
finds a correspondence in the fluid description. In this work we employ
extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free
surfaces, and moving boundaries. The models allows for a full coupling of the
phases, but in a simplified way. An experimental validation is given by an
example of gravity driven flow of a particle suspension
Nonlinear Boltzmann equation for the homogeneous isotropic case: Minimal deterministic Matlab program
The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic
model for many applications in thermodynamics, econophysics and sociodynamics.
Despite recent hardware improvements, the solution of the Boltzmann equation
remains extremely challenging from the computational point of view, in
particular by deterministic methods (free of stochastic noise). This work aims
to improve a deterministic direct method recently proposed [V.V. Aristov,
Kluwer Academic Publishers, 2001] for solving the HIBE with a generic
collisional kernel and, in particular, for taking care of the late dynamics of
the relaxation towards the equilibrium. Essentially (a) the original problem is
reformulated in terms of particle kinetic energy (exact particle number and
energy conservation during microscopic collisions) and (b) the computation of
the relaxation rates is improved by the DVM-like correction, where DVM stands
for Discrete Velocity Model (ensuring that the macroscopic conservation laws
are exactly satisfied). Both these corrections make possible to derive very
accurate reference solutions for this test case. Moreover this work aims to
distribute an open-source program (called HOMISBOLTZ), which can be
redistributed and/or modified for dealing with different applications, under
the terms of the GNU General Public License. The program has been purposely
designed in order to be minimal, not only with regards to the reduced number of
lines (less than 1,000), but also with regards to the coding style (as simple
as possible).Comment: 35 pages, 4 figures, it describes the code HOMISBOLTZ to be
distributed with the pape
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