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Published in David M Kelly, Aggelos Dimakopoulos, Pablo Higuera, Advanced Numerical Modelling of Wave Structure Interactions, 2021
David M Kelly, Aggelos Dimakopoulos, Pablo Higuera
The lattice Boltzmann method (LBM) (Succi, 2001; Frandsen, 2008; Janssen and Krafczyk, 2011) is a promising approach which is derived from the Lattice Gas Automata (LGA) method, a cellular automaton molecular dynamics model developed in the late 1980s. Despite being a discrete method, the traditional macroscopic NS equations can be derived with LGA, in which the particles in LBM move on a fixed lattice, and at every time step they undergo two processes: propagation and collision.
Multi Relaxation Time Lattice Boltzmann Method Simulation of Natural Convection Combined with Surface Radiation in a Square Open Cavity from Three Discrete Heat Sources
Published in Heat Transfer Engineering, 2021
Mustapha Ouahas, Abdelkhalek Amahmid, Mohammed Hasnaoui, Abdelfattah El Mansouri, Youssef Dahani
The Lattice-Boltzmann method, initially derived from the Lattice-Gas-Automata, has become popular to simulate different kinds of fluid dynamics problems during the last decade. This method is based on the resolution of the equation proposed by He and Luo [21]: where is a complex and nonlinear (nonlinear in terms of the discrete density distribution function ) operator, describing the collision of the particles. For the sake of simplicity, the linearization of the collision operator was based on the Bhatnagar–Gross–Krook (BGK) approximation [21]. The basic idea behind this approach is that during the collision process, the particles relax from their pre-collision state toward an equilibrium state represented by the equilibrium distribution function For two-dimensional flows, Figure 2a shows the D2Q9 model, which is the commonly used lattice model for 2D studies. This model is limited to nine discrete directions () corresponding to nine discrete velocities, given by Eq. (2) [22]:
Potential field cellular automata model for overcrowded pedestrian flow
Published in Transportmetrica A: Transport Science, 2020
Peng Zhang, Xiao-Yang Li, Hua-Yu Deng, Zhi-Yang Lin, Xiao-Ning Zhang, S. C. Wong
Pedestrian dynamics have attracted researchers in many disciplines. From a macroscopic view, pedestrian flow is considered a continuum, and hydrodynamic equations are used for modeling (Hughes 2002; Hoogendoorn and Bovy 2004; Huang et al. 2009; Xia, Wong, and Shu 2009; Jiang et al. 2010; Xiong et al. 2011). From a microscopic view, pedestrians are particles in motion. In a many-particle or social-force model (Helbing and Molnár 1995; Helbing et al. 2001; Helbing 2001), accelerations of all ‘particles’ are established to constitute an ordinary differential system, which takes into account the self-driven force of each particle to the destination and the repulsive forces among all particles. The social-force model is widely applied to many practical problems, e.g. in Porter, Hamdar, and Daamen (2018) and Zhou et al. (2019). In a cellular automaton (CA) model (Burstedde et al. 2001; Kirchner and Schadschneider 2002; Kirchner, Nishinari, and Schadschneider 2003; Nishinari et al. 2004; Varas et al. 2007; Kirik, Yurgel'yan, and Krouglov 2009; Huang and Guo 2008; Kretz 2009, 2010; Hartmann 2010; Zhang et al. 2012), also called a lattice-gas automaton model (see Kuang et al. 2008, 2014; Li and Dong 2012, and the references therein), the walking domain is divided into grid cells and a ‘particle’ updates its position at each time step. In general, pedestrian flow is analogous to vehicular flow in terms of follow-the-leader and self-organized behavior. However, the problem is two-dimensional and pedestrians' path-choice strategy is essential for modeling.
Mixed convection in an insulated rectangular enclosure with two obstacles subject to various configurations using multi-relaxation-time lattice Boltzmann method
Published in Waves in Random and Complex Media, 2022
Humayoun Shahid, Iqra Yaqoob, Waqar Azeem Khan, Madiha Aslam
Bergman and Ramadthyani [42] scruitnized the combined effect of buoyancy and thermocapillary action inside a square enclosure. The result shows that surface tension causes adaptation in the natural convective flow of the fluid. The Lattice Boltzmann method was derived from the Lattice gas automata. In this method, the Navier–Stokes equations are used for the temporal evolution of the motion of the fluid. LBM is a mesoscopic method that uses a distribution function to find the probability of a particle at a particular position, its velocity, etc. The method consists of collision and streaming of fluid particles at the lattice nodes. It deals with particle distribution rather than the single particle. The main features of LBM include computational efficiency, versatility, parallel computing, and its accuracy of prediction. The hyperbolic nature of the Lattice Boltzmann equation increases its potency. Although (LBM) has proved inefficient in dealing with the non-Newtonian fluids due to the relationship between viscosity and time relaxation. Researchers confront this problem while solving energy equations for such fluids. The insertion of the equilibrium distribution function for the modification of LBE was nominated by Fu et al. [43, 44]. Thus the equilibrium distribution function varies with nodes and directions with the constant relaxation time. On account of the independence of this method on relaxation time, it has emerged as the more effective scheme to solve energy equations in non-Newtonian fluids. Hence grid independence and validity of this method have made it more convenient than traditional LBM. In the field of continuum mechanics, three-dimensional LBE was derived by Huilgol and Kefayati [45]. This method can be applied to all fluids. Types of fluids are viscoelastic, viscoplastic, non-Newtonian, or power-law fluids. Lattice Boltzmann Method (LBM) is further modified into Two-Relaxation-Time LBM and Multi-Relaxation-Time LBM to improve its order of convergence. MRT-LBM has more numerical stability and has a higher order of accuracy as compared to the SRT-LBM [46]. The present work will numerically simulate the mixed convection heat transfer taking a lid-driven rectangular cavity. Two square obstacles set at different temperatures are placed inside the enclosure. The walls of the enclosure are insulated. Flow and thermal field simulation is done by using and models of Lattice arrangements of MRT-LBM, respectively. The effect of different dimensionless parameters like Gr, Ri, Pr and different sizes of the obstacles for different aspect ratios on the flow and temperature regimes is also studied. We have calculated Nussselt number (Nu) and average Nusselt number on the heated square obstacle. Also, we have plotted the cross-sectional velocities along the horizontal and vertical axes of the cavity.