Journal ArticleDOI
Local second-order boundary methods for lattice Boltzmann models
I. Ginzbourg,D. d'Humières +1 more
TLDR
In this paper, a new way to implement solid obstacles in lattice Boltzmann models is presented, where unknown populations at the boundary nodes are derived from the locally known populations with the help of a second-order Chapman-Enskog expansion and Dirichlet boundary conditions with a given momentum.Abstract:
A new way to implement solid obstacles in lattice Boltzmann models is presented. The unknown populations at the boundary nodes are derived from the locally known populations with the help of a second-order Chapman-Enskog expansion and Dirichlet boundary conditions with a given momentum. Steady flows near a flat wall, arbitrarily inclined with respect to the lattice links, are then obtained with a third-order error. In particular, Couette and Poiseuille flows are exactly recovered without the Knudsen layers produced for inclined walls by the bounce back condition.read more
Citations
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BookDOI
Lattice-Gas Cellular Automata and Lattice Boltzmann Models
TL;DR: In this paper, the authors provide an introduction to lattice gas cellular automata (LGCA) and lattice Boltzmann models (LBM) for numerical solution of nonlinear partial differential equations.
Journal ArticleDOI
Lattice-Boltzmann Simulations of Particle-Fluid Suspensions
Anthony J. C. Ladd,Rolf Verberg +1 more
TL;DR: In this paper, a review of applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions is presented, together with some of the important applications of these methods.
Journal ArticleDOI
Momentum transfer of a Boltzmann-lattice fluid with boundaries
TL;DR: In this article, the velocity boundary condition for curved boundaries in the lattice Boltzmann equation (LBE) was studied for moving boundaries by combination of the "bounce-back" scheme and spatial interpolations of first or second order.
Journal ArticleDOI
Viscous flow computations with the method of lattice Boltzmann equation
TL;DR: In this paper, the lattice Boltzmann equation (LBE) is applied to high Reynolds number incompressible flows, some critical issues need to be addressed, noticeably flexible spatial resolution, boundary treatments for curved solid wall, dispersion and mode of relaxation, and turbulence model.
Book
Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction
TL;DR: This book provides an introduction for graduate students and researchers of lattice-gas cellular automata and lattice Boltzmann models for the numerical solution of nonlinear partial differential equations.
References
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Book
Boundary layer theory
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Journal ArticleDOI
Lattice BGK Models for Navier-Stokes Equation
TL;DR: In this article, the Navier-Stokes equation is obtained from the kinetic BGK equation at the second-order approximation with a properly chosen equilibrium distribution, with a relaxation parameter that influences the stability of the new scheme.
Journal ArticleDOI
Numerical simulations of particulate suspensions via a discretized boltzmann equation: part 1. theoretical foundation
TL;DR: In this article, a general technique for simulating solid-fluid suspensions is described, which combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping flow regime and at higher Reynolds numbers.
Journal ArticleDOI
The lattice Boltzmann equation: theory and applications
TL;DR: The basic elements of the theory of the lattice Boltzmann equation, a special lattice gas kinetic model for hydrodynamics, are reviewed in this paper, together with some generalizations which allow one to extend the range of applicability of the method to a number of fluid dynamics related problems.
Journal ArticleDOI
Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method.
TL;DR: This paper shows that both of these effects of a non-Galilean invariance caused by a density-dependent coefficient in the convection term can be eliminated exactly in a lattice Boltzmann-equation model.
Related Papers (5)
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