Initial and Boundary Conditions for the Lattice Boltzmann Method

A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical performance of the lattice Boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method. The discretization error of the lattice Boltzmann method decreases quadratically with finer resolution both in space and in time. The roundoff error of the lattice Boltzmann method creates problems unless double precision arithmetic is used.Comment: 42 pages in Postscript, with additional 27 Postscript figures Physical Review E, Submitted December 92, Revised June 9

Axisymmetric multiphase lattice Boltzmann method

A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [ Phys. Rev. E 47 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equations is demonstrated analytically by means of a Chapmann-Enskog expansion and numerically through several test cases. In particular, the model is benchmarked for its accuracy in reproducing the dynamics of the oscillations of an axially symmetric droplet and on the capillary breakup of a viscous liquid thread. Very good quantitative agreement between the numerical solutions and the analytical results is observed

Lattice Boltzmann method for viscoelastic fluids

Lattice Boltzmann model for viscoelastic flow simulation is proposed; elastic effects are taken into account in the framework of Maxwell model. The following three examples are studied using the proposed approach: a transverse velocity autocorrelation function for free evolving system with random initial velocities, a boundary-driven propagating shear waves, and a resonant enhancement of oscillations in a periodically driven fluid in a capillary. The measured shear wave dispersion relation is found to be in a good agreement with the theoretical one derived for the Navier-Stokes equation with the Maxwell viscoelastic term.Comment: 4 pages, 5 figure

Matrix-valued Quantum Lattice Boltzmann Method

We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum Boltzmann equation, with the classical Maxwell distribution replaced by Fermi-Dirac functions. To accommodate the spin density matrix, the distribution functions become 2 x 2 matrix-valued. From an analytic perspective, the efficient, commonly used BGK approximation of the collision operator is valid in the present setting. The numerical scheme could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics.Comment: 18 page

Lattice-Boltzmann Method for Geophysical Plastic Flows

We explore possible applications of the Lattice-Boltzmann Method for the simulation of geophysical flows. This fluid solver, while successful in other fields, is still rarely used for geotechnical applications. We show how the standard method can be modified to represent free-surface realization of mudflows, debris flows, and in general any plastic flow, through the implementation of a Bingham constitutive model. The chapter is completed by an example of a full-scale simulation of a plastic fluid flowing down an inclined channel and depositing on a flat surface. An application is given, where the fluid interacts with a vertical obstacle in the channel.Comment: in W. Wu, R.I. Borja (Edts.) Recent advances in modelling landslides and debris flow, Springer Series in Geomechanics and Geoengineering (2014), ISBN 978-3-319-11052-3, pp. 131-14