【物理应用】基于Matlab实现LBM-D2Q9模型粗糙界面流动

1 内容介绍

采用D2Q9模型，反弹边界，粗糙界面采用规则矩形

2 仿真代码

%%lbm方法模拟粗糙界面流动程序，

%%采用D2Q9模型，反弹边界，粗糙界面采用规则矩形

clear all;

clc;

%++++++++++++++++++++++++++++++++++++++++++++++++++++++++??????????????????????+++++++++++++++++++++++++++++++++++++++++

nx=40; ny=250;

bound=zeros(nx,ny);bound([1 nx],:)=1;A=1:38;

left_corner=zeros(1,5);right_corner=zeros(1,5);

for i=1:5

   bound_point=40*i+(0:10);

   bound(1:6,bound_point)=1;

   bound(nx-(1:5),bound_point)=1;

   left_corner(i)=40*i;

   right_corner(i)=40*i+10;

   A=[A ((40*i+1):(40*i+9)) (40*i+12):(40*(i+1)-2)];

end

A=[A A(end)+1:250];

B=bwboundaries(bound,8);

B1=B{1};B2=B{2};

B1(1:249,:)=[];B2(end-248:end,:)=[];

[~,tempi,~]=intersect(B1(:,2),A);b1=B1(tempi,:);

[~,tempi,~]=intersect(B2(:,2),A);b2=B2(tempi,:);

boundary=find(bound==1);

imshow(1-bound);

figure;  

%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++????????????+++++++++++++++++++++++++++++++++++++++++

Pin=1.001;Pout=1;

Rb=0.7;

tau= 1;

dx=1;dy=1;dt=1;c=dx/dt;t1=4/9; t2=1/9; t3=1/36; c_squ=c^2/3;  

rouin=Pin/c_squ; rouout=Pout/c_squ;

DENSITY=rouout*ones(nx,ny);DENSITY(:,1)=rouin*ones(nx,1);

DENSITY(boundary)=rouout;

UX = zeros(nx,ny);UY= zeros(nx,ny);UX0=zeros(nx,ny);UY0=zeros([nx ny]);DENSITY0=zeros(nx,ny);

3 运行结果

4 参考文献

[1]刘立军, 胡文彬, 梅红岩. 基于变精度粗糙集模型的Matlab实现[J]. 计算机工程与应用, 2007.

[2]徐辉, 陶文铨. 熵格子Boltzmann方法模拟高Reynolds数流动[J]. 工程热物理学报, 2009(1):3.

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