The Application Of Lattice Boltzmann Method

In the past two decades,a new scheme——lattice Boltzmann method,which is different from conventional computational fluid dynamics(CFD),has been developed quickly.Lattice Boltzmann method was first proposed to simulate fluid dynamics by McNamara and Zanetti in 1988.It comes from Lattice Gas Automata(LGA), and can be regarded as an extension of the lattice gas automaton or a special discrete form of the continous Boltzmann equation for kinetic theory.Conventional numerical schemes are based on the discretization of macroscopic equations,while the lattice Boltzmann method is based on statistical physics.It describes the microscopic picture of particles movement in an extremely simplified way,and gives a macroscopic fluid movement.This characteristic makes lattice Boltzmann method may become a bridge communicated between microscope and macroscope.For many advantages,including simple calculation,parallel process etc.,Lattice Boltzmann method has developed rapidly since it appeared.This thesis is discussed focusing on the Lattice Boltzmann method.Starting with the characters,history,applications and development of Lattice Boltzmann method.Then introduce some classical lattice Boltzmann models,including DnQm models,He's and Guo's models for incompressible Navier-Stikes equation and Zhou's model for shallow water equation.For the application of Lattice Boltzmann method on nonlinear equations,Yan's lattice Boltzmann model of Burgers' equation is introduced firstly.In his model,the equilibrium distributions are no longer decided by the physics characters in the view of microscope,but the Chapman-Enskog expansion with the macroscopic equation.This idea enlarges the application area of lattice Boltzmann method.And lattice Boltzmann method is applied to simulate many other nonlinear equations after Yan's work.Especially,for the red-green model in traffic flow,we introduce it's origin and theory analysis,give the lattice Boltzmann method,the stability of the method and the numerical result which compared with other schemes.For the boundary condition whick plays an important role in the fluid dynamics. The boundary condition is changed from non-slip to slip(part-slip) while the view point changed from macroseope to microscope(i.e.Kn number from less than 0 to 0.1).For lattice Boltzmann method,most of the existing boundary schemes are used for non-slip or slip(part-slip) for some special angles.There is no boundary treatment for slip(part-slip) condition on curved boundary.In this thesis,some boundary schemes,including bounce-back scheme,kinetic scheme etc.will be introduced, some non-slip treatment on curved boundary and slip treatment on the special angle will also be introduced.Based on the existing scheme,we try to treat part-slip case on curved boundary,we design it,and analyze why it doesn't work as expectation.This work will give some advices for future works.For the theory of lattice Boltzmann method,there are some good work on it,but is still not perfect on the whole.Stability and truncation error analysis of lattice Boltzmann method will be breifly introduced.Author gate the truncation analysis for the shallow water equation by emulating the idea of Holdych's truncation analysis.It will not included for the length limit of the thesis.Our work is outlined in the following several aspects.For the lattice Boltzmann method of shallow water equation,we find that the method can't work for large depth-ratio case in the test of dam break.Some explanations are given,and jetforced flow as a new numerical example will be tested.For the red-green model in traffic flow,Lattice Boltzmann method is applied to this model.The stability of method is given.The numerical result is given and compared with other method. The comparation shows effective of the method.Some attempts are designed for part-slip condition on curved boundary.Though them don't work as we expected, some usefull guidance are gived by analysis for the future works.