113 research outputs found
Body-force modelling in thermal compressible flows with lattice Boltzmann method
Body force modelling in lattice Boltzmann method (LBM) has been extensively
studied in the incompressible limit but rarely discussed for thermal
compressible flows. Here we present a systematic approach of incorporating body
force in LBM which is valid for thermal compressible and non-equilibrium flows.
In particular, a LBM forcing scheme accurate for the energy equation with
second-order time accuracy is given. New and essential in this scheme is the
third-moment contribution of the force term. It is shown via Chapman-Enskog
analysis that the absence of this contribution causes an erroneous heat flux
quadratic in Mach number and linear in temperature variation. The theoretical
findings are verified and the necessity of the third-moment contribution
demonstrated by numerical simulations
Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows
A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0:5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations that have been chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased
Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation
We present a further theoretical extension to the kinetic theory based
formulation of the lattice Boltzmann method of Shan et al (2006). In addition
to the higher order projection of the equilibrium distribution function and a
sufficiently accurate Gauss-Hermite quadrature in the original formulation, a
new regularization procedure is introduced in this paper. This procedure
ensures a consistent order of accuracy control over the non-equilibrium
contributions in the Galerkin sense. Using this formulation, we construct a
specific lattice Boltzmann model that accurately incorporates up to the third
order hydrodynamic moments. Numerical evidences demonstrate that the extended
model overcomes some major defects existed in the conventionally known lattice
Boltzmann models, so that fluid flows at finite Knudsen number (Kn) can be more
quantitatively simulated. Results from force-driven Poiseuille flow simulations
predict the Knudsen's minimum and the asymptotic behavior of flow flux at large
Kn
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
Fundamental Conditions for N-th Order Accurate Lattice Boltzmann Models
In this paper, we theoretically prove a set of fundamental conditions
pertaining discrete velocity sets and corresponding weights. These conditions
provide sufficient conditions for a priori formulation of lattice Boltzmann
models that automatically admit correct hydrodynamic moments up to any given
N-th order
Structure and isotropy of lattice pressure tensors for multirange potentials
We systematically analyze the tensorial structure of the lattice pressure
tensors for a class of multi-phase lattice Boltzmann models (LBM) with
multi-range interactions. Due to lattice discrete effects, we show that the
built-in isotropy properties of the lattice interaction forces are not
necessarily mirrored in the corresponding lattice pressure tensor. This finding
opens a different perspective for constructing forcing schemes, achieving the
desired isotropy in the lattice pressure tensors via a suitable choice of
multi-range potentials. As an immediate application, the obtained LBM forcing
schemes are tested via numerical simulations of non-ideal equilibrium
interfaces and are shown to yield weaker and less spatially extended spurious
currents with respect to forcing schemes obtained by forcing isotropy
requirements only. From a general perspective, the proposed analysis yields an
approach for implementing forcing symmetries, never explored so far in the
framework of the Shan-Chen method for LBM. We argue this will be beneficial for
future studies of non-ideal interfaces.Comment: 14 pages + Appendix, 8 figures; updated to published version: added
figures and tex
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