Automatic grid refinement criterion for lattice Boltzmann method

In all kinds of engineering problems, and in particular in methods for computational fluid dynamics based on regular grids, local grid refinement is of crucial importance. To save on computational expense, many applications require to resolve a wide range of scales present in a numerical simulation by locally adding more mesh points. In general, the need for a higher (or a lower) resolution is not known a priori, and it is therefore difficult to locate areas for which local grid refinement is required. In this paper, we propose a novel algorithm for the lattice Boltzmann method, based on physical concepts, to automatically construct a pattern of local refinement. We apply the idea to the two-dimensional lid-driven cavity and show that the automatically refined grid can lead to results of equal quality with less grid points, thus sparing computational resources and time. The proposed automatic grid refinement strategy has been implemented in the parallel open-source library Palabos

A lattice Boltzmann model for natural convection in cavities

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment–based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second–order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 106. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy

SBoTFlow: A Scalable framework using lattice Boltzmann method and Topology-confined mesh refinement for moving-body applications

This paper proposes a scalable lattice-Boltzmann computational framework (SBoTFlow) for simulations of flexible moving objects in an incompressible fluid flow. Behavior of fluid flow formed from moving boundaries of flexible-object motions is obtained through the multidirect forcing immersed boundary scheme associated with the lattice Boltzmann equation with a parallel topology-confined block refinement framework. We first demonstrate that the hydrodynamic quantities computed in this manner for standard benchmarks, including the Tayler-Green vortex flow and flow over an obstacle-embedded lid-driven cavity and an isolated circular cylinder, agree well with those previously published in the literature. We then exploit the framework to probe the underlying dynamic properties contributing to fluid flow under flexible motions at different Reynolds numbers by simulating large-scale flapping wing motions of both amplitude and frequency. The analysis shows that the proposed numerical framework for pitching and flapping motions has a strong ability to accurately capture high amplitudes, specifically up to $64^\circ$, and a frequency of $f=1/2.5\pi$. This suggests that the present parallel numerical framework has the potential to be used in studying flexible motions, such as insect flight or wing aerodynamics

A Lifting Relation from Macroscopic Variables to Mesoscopic Variables in Lattice Boltzmann Method: Derivation, Numerical Assessments and Coupling Computations Validation

In this paper, analytic relations between the macroscopic variables and the mesoscopic variables are derived for lattice Boltzmann methods (LBM). The analytic relations are achieved by two different methods for the exchange from velocity fields of finite-type methods to the single particle distribution functions of LBM. The numerical errors of reconstructing the single particle distribution functions and the non-equilibrium distribution function by macroscopic fields are investigated. Results show that their accuracy is better than the existing ones. The proposed reconstruction operator has been used to implement the coupling computations of LBM and macro-numerical methods of FVM. The lid-driven cavity flow is chosen to carry out the coupling computations based on the numerical strategies of domain decomposition methods (DDM). The numerical results show that the proposed lifting relations are accurate and robust

Dynamic density functional theory versus Kinetic theory of simple fluids

By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on the evolution of the one particle phase space distribution, rather than on the evolution of the average particle density, which features in dynamic density functional theory. The resulting equation can be studied in two different physical limits: diffusive dynamics, typical of colloidal fluids without hydrodynamic interaction, where particles are subject to overdamped motion resulting from the coupling with a solvent at rest, and inertial dynamics, typical of molecular fluids. Finally, we propose an algorithm to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.Comment: 15 page