1,237 research outputs found
Moment-based formulation of Navier–Maxwell slip boundary conditions for lattice Boltzmann simulations of rarefied flows in microchannels
We present an implementation of first-order Navier–Maxwell slip boundary conditions for simulating near-continuum rarefied flows in microchannels with the lattice Boltzmann method. Rather than imposing boundary conditions directly on the particle velocity distribution functions, following the existing discrete analogs of the specular and diffuse reflection conditions from continuous kinetic theory, we use a moment-based method to impose the Navier–Maxwell slip boundary conditions that relate the velocity and the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the\ud
domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. The results are in excellent agreement with asymptotic solutions of the compressible Navier-Stokes equations for microchannel flows in the slip regime. Our moment formalism is also valuable for analysing the existing boundary conditions, and explains the origin of numerical slip in the bounce-back and other common boundary conditions that impose explicit conditions on the higher moments instead of on the local tangential velocity
A lattice Boltzmann model for natural convection in cavities
We study a multiple relaxation time lattice Boltzmann model for natural convection with moment–based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second–order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 106. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy
Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann
On-site boundary conditions are often desired for lattice Boltzmann
simulations of fluid flow in complex geometries such as porous media or
microfluidic devices. The possibility to specify the exact position of the
boundary, independent of other simulation parameters, simplifies the analysis
of the system. For practical applications it should allow to freely specify the
direction of the flux, and it should be straight forward to implement in three
dimensions. Furthermore, especially for parallelized solvers it is of great
advantage if the boundary condition can be applied locally, involving only
information available on the current lattice site. We meet this need by
describing in detail how to transfer the approach suggested by Zou and He to a
D3Q19 lattice. The boundary condition acts locally, is independent of the
details of the relaxation process during collision and contains no artificial
slip. In particular, the case of an on-site no-slip boundary condition is
naturally included. We test the boundary condition in several setups and
confirm that it is capable to accurately model the velocity field up to second
order and does not contain any numerical slip.Comment: 13 pages, 4 figures, revised versio
Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions
We present a mathematical formulation of kinetic boundary conditions for
Lattice Boltzmann schemes in terms of reflection, slip, and accommodation
coefficients. It is analytically and numerically shown that, in the presence of
a non-zero slip coefficient, the Lattice Boltzmann flow develops a physical
slip flow component at the wall. Moreover, it is shown that the slip
coefficient can be tuned in such a way to recover quantitative agreement with
analytical and experimental results up to second order in the Knudsen number.Comment: 27 pages, 4 figure
Detailed analysis of the lattice Boltzmann method on unstructured grids
The lattice Boltzmann method has become a standard for efficiently solving
problems in fluid dynamics. While unstructured grids allow for a more efficient
geometrical representation of complex boundaries, the lattice Boltzmann methods
is often implemented using regular grids. Here we analyze two implementations
of the lattice Boltzmann method on unstructured grids, the standard forward
Euler method and the operator splitting method. We derive the evolution of the
macroscopic variables by means of the Chapman-Enskog expansion, and we prove
that it yields the Navier-Stokes equation and is first order accurate in terms
of the temporal discretization and second order in terms of the spatial
discretization. Relations between the kinetic viscosity and the integration
time step are derived for both the Euler method and the operator splitting
method. Finally we suggest an improved version of the bounce-back boundary
condition. We test our implementations in both standard benchmark geometries
and in the pore network of a real sample of a porous rock.Comment: 42 page
Shear stress in lattice Boltzmann simulations
A thorough study of shear stress within the lattice Boltzmann method is
provided. Via standard multiscale Chapman-Enskog expansion we investigate the
dependence of the error in shear stress on grid resolution showing that the
shear stress obtained by the lattice Boltzmann method is second order accurate.
This convergence, however, is usually spoiled by the boundary conditions. It is
also investigated which value of the relaxation parameter minimizes the error.
Furthermore, for simulations using velocity boundary conditions, an artificial
mass increase is often observed. This is a consequence of the compressibility
of the lattice Boltzmann fluid. We investigate this issue and derive an
analytic expression for the time-dependence of the fluid density in terms of
the Reynolds number, Mach number and a geometric factor for the case of a
Poiseuille flow through a rectangular channel in three dimensions. Comparison
of the analytic expression with results of lattice Boltzmann simulations shows
excellent agreement.Comment: 15 pages, 4 figures, 2 table
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