3D Simulation of Self-Compacting Concrete Flow Based on MRT-LBM

A three-dimensional multiple-relaxation-time lattice Boltzmann method (MRT-LBM) with a D3Q27 discrete velocity model is applied for simulation of self-compacting concrete (SCC) flows. In the present study, the SCC is assumed as a non-Newtonian fluid, and a modified Herschel–Bulkley model is used as constitutive mode. The mass tracking algorithm was used for modeling the liquid-gas interface. Two numerical examples of the slump test and enhanced L-box test were performed, and the calculated results are compared with available experiments in literatures. The numerical results demonstrate the capability of the proposed MRT-LBM in modeling of self-compacting concrete flows.

Boundary Layers and Shock Profiles for the Broadwell Model

We consider the existence of nonlinear boundary layers and the typically nonlinear problem of existence of shock profiles for the Broadwell model, which is a simplified discrete velocity model for the Boltzmann equation. We find explicit expressions for the nonlinear boundary layers and the shock profiles. In spite of the few velocities used for the Broadwell model, the solutions are (at least partly) in qualitatively good agreement with the results for the discrete Boltzmann equation, that is the general discrete velocity model, and the full Boltzmann equation.

Lattice Boltzmann kinetic modeling and simulation of thermal liquid–vapor system

We present a highly efficient lattice Boltzmann (LB) kinetic model for thermal liquid–vapor system. Three key components are as below: (i) a discrete velocity model (DVM) by Kataoka et al. [Phys. Rev. E69, 035701(R) (2004)]; (ii) a forcing term Ii aiming to describe the interfacial stress and recover the van der Waals (VDW) equation of state (EOS) by Gonnella et al. [Phys. Rev. E76, 036703 (2007)] and (iii) a Windowed Fast Fourier Transform (WFFT) scheme and its inverse by our group [Phys. Rev. E84, 046715 (2011)] for solving the spatial derivatives, together with a second-order Runge–Kutta (RK) finite difference scheme for solving the temporal derivative in the LB equation. The model is verified and validated by well-known benchmark tests. The results recovered from the present model are well consistent with previous ones [Phys. Rev. E84, 046715 (2011)] or theoretical analysis. The usage of less discrete velocities, high-order RK algorithm and WFFT scheme with 16th-order in precision makes the model more efficient by about 10 times and more accurate than the original one.

On the Generation of a Hexagonal Collision Model for the Boltzmann equation

In this article we prove the existence of two different classes of regular hexagons in the hexagonal grid. We develop a generalized layer-wise construction of a hexagonal discrete velocity model and derive general formulae to identify all regular hexagons belonging to the grid. We also present some numerical results based on the hexagonal grid.

A DIFFUSIVE LIMIT FOR NONLINEAR DISCRETE VELOCITY MODELS

This paper is devoted to the analysis of the diffusive limit for a general discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighbourhood of global Maxwellians. The scaled solutions of discrete Boltzmann equation are shown to have fluctuations that converge locally in time weakly to a limit governed by a solution of incompressible Stokes equations provided that the initial fluctuations are smooth. The weak limit becomes strong when the initial fluctuations converge to appropriate initial data. As applications the Carleman model and the one-dimensional Broadwell model are analyzed in detail.