اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn Onsager-like Relation for the Lattice Boltzmann Method
240
0
0.0
(
0
)
تأليف
Wen-an Yong
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
An Onsager-like relation is proposed as a new criterion for constructing and analysing the lattice Boltzmann (LB) method. For LB models obeying the relation, we analyse their linearized stability, establish their diffusive limit, and find new constraints for those with free parameters. The new relation seems of fundamental importance for the LB method.
قيم البحث
اقرأ أيضاً
We propose a novel approach to the numerical simulation of thin film flows, based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin film equations are recovered and perform validation
tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop towards its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied, and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem of a droplet sliding on an inclined plane, finding that the Capillary number scales linearly with the Bond number, in agreement with experimental results. At last, we demonstrate the ability of the method to handle heterogenous and complex systems by showcasing the controlled dewetting of a thin film on a chemically structured substrate.
In this paper, we first present a unified framework for the modelling of generalized lattice Boltzmann method (GLBM). We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct Taylor expansi
on and recurrence equations approaches) that have been used to obtain the macroscopic Navier-Stokes equations and nonlinear convection-diffusion equations from the GLBM, and show that from mathematical point of view, these four analysis methods are equivalent to each other. Finally, we give some elements that are needed in the implementation of the GLBM, and also find that some available LB models can be obtained from this GLBM.
In this paper, a diffuse-interface lattice Boltzmann method (DI-LBM) is developed for fluid-particle interaction problems. In this method, the sharp interface between the fluid and solid is replaced by a thin but nonzero thickness transition region n
amed diffuse interface, where the physical variables varies continuously. In order to describe the diffuse interface, we introduce a smooth function, which is similar to the order parameter in phase-field model or the volume fraction of solid phase in the partially saturated lattice Boltzmann method (PS-LBM). In addition, to depict the fluid-particle interaction more accurately, a modified force term is also proposed and included in the evolution equation of the DI-LBM. Some classical problems are used to test the DI-LBM, and the results are in good agreement with some available theoretical and numerical works. Finally, it is also found that the DI-LBM is more efficient and accurate than the PS-LBM with the superposition model.
Central moment lattice Boltzmann method (LBM) is one of the more recent developments among the lattice kinetic schemes for computational fluid dynamics. A key element in this approach is the use of central moments to specify collision process and for
cing, and thereby naturally maintaining Galilean invariance, an important characteristic of fluid flows. When the different central moments are relaxed at different rates like in a standard multiple relaxation time (MRT) formulation based on raw moments, it is endowed with a number of desirable physical and numerical features. Since the collision operator exhibits a cascaded structure, this approach is also known as the cascaded LBM. While the cascaded LBM has been developed sometime ago, a systematic study of its numerical properties, such as accuracy, grid convergence and stability for well defined canonical problems is lacking and the present work is intended to fulfill this need. We perform a quantitative study of the performance of the cascaded LBM for a set of benchmark problems of differing complexity, viz., Poiseuille flow, decaying Taylor-Green vortex flow and lid-driven cavity flow. We first establish its grid convergence and demonstrate second order accuracy under diffusive scaling for both the velocity field and its derivatives, i.e. components of the strain rate tensor, as well. The method is shown to quantitatively reproduce steady/unsteady analytical solutions or other numerical results with excellent accuracy. Numerical experiments further demonstrate that the central moment MRT LBM results in significant stability improvements when compared with certain existing collision models at moderate additional computational cost.
In this article, a coupled Two-relaxation-time Lattice Boltzmann-Volume penalization (TRT-LBM-VP) method is presented to simulate flows past obstacles. Two relaxation times are used in the collision operator, of which one is related to the fluid visc
osity and the other one is related to the numerical stability and accuracy. The volume penalization method is introduced into the TRT-LBM by an external forcing term. In the procedure of the TRT-LBM-VP, the processes of interpolating velocities on the boundaries points and distributing the force density to the Eulerian points are unneeded. Performing the TRT-LBM-VP on a certain point, only the variables of this point are needed. As a consequence, the TRT-LBM-VP can be conducted parallelly. From the comparison between the result of the cylindrical Couette flow solved by the TRT-LBM-VP and that solved by the Single-relaxation-time LBM-VP (SRT-LBM-VP), the accuracy of the TRT-LBM-VP is higher than that of the SRT-LBM-VP. Flows past a single circular cylinder, a pair of cylinders in tandem and side-by-side arrangements, two counter-rotating cylinders and a NACA-0012 airfoil are chosen as numerical experiments to verify the present method further. Good agreements between the present results and those in the previous literatures are achieved.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
