In this paper, a discrete velocity model and a lattice Boltzmann model are proposed for binary mixtures of nonideal fluids based on the Enskog theory. The velocity space of the Enskog equation for each component is first discretized by applying a Gaussian quadrature, resulting in a discrete velocity model that can be solved by suitable numerical schemes. A lattice Boltzmann model is then derive...

The lattice Boltzmann method (LBM) is used in computational fluid mechanics (CFD) to simulate flows. Introduced by McNamara [3] the LBM historically is based on lattice gas automata. Instead simulating each particle a statistical average for a sufficient small control volume is applied. The LBM can also be considered as the solution to a velocity-discrete Boltzmann equation with an appropriate ...

A new immersed boundary-lattice Boltzmann method (IB-LBM) is proposed and validated in this work by its application to simulate incompressible viscous flows. The conventional IB-LBM based on the lattice Boltzmann equation with external forcing term, which contains a boundary velocity to represent the effect that the moving boundary exerts on the bounce-back distribution functions, whereas the p...

In this paper we describe an extension of a recently developed lattice Boltzmann method for solving the advection–diffusion equation. Our proposed approach allows to couple grids of different grid resolutions and includes a staggered timestepping scheme, interpolations in space and time and finally a scaling step ensuring the continuity of the desired macroscopic quantities across the grid inte...

We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid-gas density ratios up to 10. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation equations. We validate the model by showing that a stationary droplet obeys the Young-Laplace law...

We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture t...

A graphic processing unit GPU implementation of the multicomponent lattice Boltzmann equation with multirange interactions for soft-glassy materials “glassy” lattice Boltzmann LB is presented. Performance measurements for flows under shear indicate a GPU/CPU speed up in excess of 10 for 10242 grids. Such significant speed up permits to carry out multimillion time-steps simulations of 10242 grid...

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recove...

Recently Reis and Phillips [Phys. Rev. E 77, 026702 (2008)] proposed a perturbative method to solve the dispersion equation derived from the linearized lattice Boltzmann equation. We will demonstrate that the method proposed by Reis and Phillips is a reinvention of an existing method. We would also like to refute a number of claims made by Reis and Phillips.

We report progress in constructing Boltzmann weights for integrable 3dimensional lattice spin models. We show that a large class of vertex solutions to the modified tetrahedron equation can be conveniently parameterized in terms of N -th roots of theta-functions on the Jacobian of a compact algebraic curve. Fay’s identity guarantees the Fermat relations and the classical equations of motion for...