Theory of the lattice Boltzmann equation: symmetry properties of discrete velocity sets.

نویسندگان

  • Robert Rubinstein
  • Li-Shi Luo
چکیده

The lattice Boltzmann equation replaces continuous particle velocity space by a finite set; the velocity distribution function then varies over a finite-dimensional vector space instead of over an infinite-dimensional function space. The number of linearly independent moments of the distribution function in a lattice Boltzmann model cannot exceed the number of velocities; finite dimensionality therefore necessarily induces linear dependences among the moments that do not exist in a continuous theory. Given a finite velocity set, it is important to know which moments are free of these dependences. Elementary group theory is applied to the solution of this problem. It is found that decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group makes it straightforward to uncover linear dependences among the moments. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing higher-dimensional models are suggested.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A hybrid scheme of single relaxation time lattice Boltzmann and finite volume methods coupled with discrete ordinates method for combined natural convection and volumetric radiation in an enclosure

This paper is focused on the application of hybrid Single relaxation time lattice Boltzmann and finite volume methods in conjunction with discrete ordinates method to simulate coupled natural convection and volumetric radiation in differentially heated enclosure, filled with an absorbing, emitting and non-scattering gray medium. In this work, the velocity and temperature fields are calculated u...

متن کامل

Numerical simulation of a three-layered radiant porous heat exchanger including lattice Boltzmann simulation of fluid flow

This paper deals with the hydrodynamic and thermal analysis of a new type of porous heat exchanger (PHE). This system operates based on energy conversion between gas enthalpy and thermal radiation. The proposed PHE has one high temperature (HT) and two heat recovery (HR1 and HR2) sections. In HT section, the enthalpy of flowing high temperature gas flow that is converted to thermal radiation em...

متن کامل

Dispersion and Deposition of Micro Particles over Two Square Obstacles in a Channel via Hybrid Lattice Boltzmann Method and Discrete Phase model

Dispersion and deposition of aerosol particles over two square cylinders confined in a channel in laminar unsteady vortical flow were investigated numerically. Lattice Boltzmann method was used to calculate fluid characteristics and modify Euler method was employed as Lagrangian particle tracing procedure to obtain particle trajectories. Drag, Saffman lift, gravity, buoyancy and Brownian motion...

متن کامل

Numerical Simulation of Fluid Flow Past a Square Cylinder Using a Lattice Boltzmann Method

The method of lattice boltzmann equation(LBE) is a kinetic-based approach for fluid flow computations. In the last decade, minimal kinetic models, and primarily the LBE, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully developed turbulence, to flow with dynamic phase transitions. In the presen...

متن کامل

Natural Convection and Entropy Generation in Γ-Shaped Enclosure Using Lattice Boltzmann Method

This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation.  A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Physical review. E, Statistical, nonlinear, and soft matter physics

دوره 77 3 Pt 2  شماره 

صفحات  -

تاریخ انتشار 2008