{"id":3167,"date":"2023-12-17T17:32:25","date_gmt":"2023-12-17T09:32:25","guid":{"rendered":"http:\/\/81.70.49.155\/?p=3167"},"modified":"2024-03-14T15:52:07","modified_gmt":"2024-03-14T07:52:07","slug":"lbm-4%e5%9c%a8%e5%8f%8d%e5%bc%b9%e8%be%b9%e7%95%8c%e5%9c%86%e6%9f%b1%e7%bb%95%e6%b5%81%e5%9f%ba%e7%a1%80%e4%b8%8a%e6%94%b9%e4%b8%baib-lbm%e7%89%88%e6%9c%ac","status":"publish","type":"post","link":"http:\/\/81.70.49.155\/?p=3167","title":{"rendered":"[LBM-4]\u5728\u53cd\u5f39\u8fb9\u754c\u5706\u67f1\u7ed5\u6d41\u57fa\u7840\u4e0a\u6539\u4e3aIB-LBM\u7248\u672c"},"content":{"rendered":"

[passster password=\"IB-LBM\" area=\"3212\"]<\/p>\n

\n\t%<\/span>\u7ea2\u8272<\/span>\u4ee3\u7801\u4e3a\u589e\u52a0\u4ee3\u7801\uff1b<\/span>\u7eff\u5e95<\/span><\/span>\u4e3a\u5c4f\u853d\u7684\u4ee3\u7801<\/span>\n<\/p>\n

\n\t%\u521d\u59cb\u5316\n<\/p>\n

clc; clear; close;  
\nlx=400;  ly=81; <\/p>\n

%\u6784\u5efa\u58c1\u9762
\nBound=zeros(lx,ly);
\nBound(:,[1,ly])=1;<\/p>\n

%\u6784\u5efa\u5706\u67f1\u8fb9\u754c<\/span>
\nxc=lx\/4;  yc=ly\/2;   Rc=10;<\/span>
\nNc=floor(2*2*pi*Rc);<\/span>
\nceta=2*pi\/Nc:2*pi\/Nc:2*pi;<\/span>
\nXcy=xc+Rc*cos(ceta); Ycy=yc+Rc*sin(ceta); <\/span>
\nds=0.5;<\/span>
\nFx=zeros(1,Nc);  Fy=zeros(1,Nc);  <\/span>
\nUxi=zeros(1,Nc); Uyi=zeros(1,Nc);  <\/span>
\nCd=[]; Cl=[];<\/span><\/p>\n

% for i=floor(xc)-7:floor(xc)+7<\/span>
\n%     for j=floor(yc)-7:floor(yc)+7<\/span>
\n%          if ((i-xc)^2+(j-yc)^2)^0.5<=Rc<\/span>
\n%              Bound(i,j)=1;<\/span>
\n%          end<\/span>
\n%     end<\/span>
\n% end<\/span><\/p>\n

% Bin=[]; BFin0=[]; BFin=[];<\/span>
\n% opposite=[1,4,5,2,3,8,9,6,7];<\/span>
\n% for i=1:lx<\/span>
\n%     for j=1:ly<\/span>
\n%        if Bound(i,j)==1<\/span>
\n%            Bin=[Bin,i+lx*(j-1)];<\/span>
\n%            for k=1:9<\/span>
\n%                BFin=[BFin,(i+lx*(j-1))+(opposite(k)-1)*lx*ly];<\/span>
\n%                BFin0=[BFin0,(i+lx*(j-1))+(k-1)*lx*ly];<\/span>
\n%            end <\/span>
\n%         end<\/span>
\n%     end<\/span>
\n% end<\/span><\/p>\n

Re=100;
\nUin=0.1;
\nyu=2*Rc*Uin\/Re;
\nfx0=0;   
\nW=[4\/9,1\/9,1\/9,1\/9,1\/9,1\/36,1\/36,1\/36,1\/36];
\nex=[0, 1, 0, -1, 0  1,-1, -1, 1];
\ney=[0, 0, 1, 0, -1, 1, 1, -1,-1];
\ncs=1\/sqrt(3);<\/p>\n

rho=ones(lx,ly);
\nu=zeros(lx,ly);
\nv=zeros(lx,ly);
\nfx=zeros(lx,ly)+fx0;
\nfy=zeros(lx,ly);
\nM1=W(1)*rho; M2=W(2)*rho; M3=W(6)*rho;
\nF= cat(3,M1,M2,M2,M2,M2,M3,M3,M3,M3);
\nFeq=F;<\/p>\n

%\u8fc1\u79fb\u4e0b\u6807
\nD2x=[lx,1:lx-1]; D2y=[1:ly];
\nD3x=[1:lx];      D3y=[ly,1:ly-1];
\nD4x=[2:lx,1];    D4y=[1:ly];
\nD5x=[1:lx];      D5y=[2:ly,1];
\nD6x=[lx,1:lx-1]; D6y=[ly,1:ly-1];
\nD7x=[2:lx,1];    D7y=[ly,1:ly-1];
\nD8x=[2:lx,1];    D8y=[2:ly,1];
\nD9x=[lx,1:lx-1]; D9y=[2:ly,1];<\/p>\n

%% \u4e3b\u5faa\u73af===========================================
\n% for tStep=1:15000<\/span>
\nfor tStep=1:25000
\n% \u8fc1\u79fb
\nF0(:,:,1)=F(:,:,1);
\nF0(:,:,2)=F(D2x,D2y,2);
\nF0(:,:,3)=F(D3x,D3y,3);
\nF0(:,:,4)=F(D4x,D4y,4);
\nF0(:,:,5)=F(D5x,D5y,5);
\nF0(:,:,6)=F(D6x,D6y,6);
\nF0(:,:,7)=F(D7x,D7y,7);
\nF0(:,:,8)=F(D8x,D8y,8);
\nF0(:,:,9)=F(D9x,D9y,9);
\nF=F0;<\/p>\n

%\u8ba1\u7b97\u5b8f\u89c2\u91cf
\nrho=sum(F,3);
\nu=(sum(F(:,:,[2,6,9]),3)-sum(F(:,:,[4,7,8]),3)).\/rho+fx\/2.\/rho;
\nv=(sum(F(:,:,[3,6,7]),3)-sum(F(:,:,[5,8,9]),3)).\/rho+fy\/2.\/rho;<\/p>\n

%\u8bbe\u7f6e\u5b8f\u89c2\u8fb9\u754c
\nrho(:,1)=1;%rho(:,2);       %\u4e0b\u58c1\u9762<\/span>
\n u(:,1)=0;  v(:,1)=0;    %<\/span><\/p>\n

rho(:,ly)=1;%rho(:,ly-1);   %\u4e0a\u58c1\u9762<\/span>
\n u(:,ly)=0;  v(:,ly)=0;    %<\/span>
\n% u(Bin)=0;  v(Bin)=0;     %\u6240\u6709\u56fa\u4f53<\/span><\/p>\n

rho(1,:)=rho(2,:);        %\u5165\u53e3<\/span>
\n u(1,:)=Uin;  v(1,:)=0;    %<\/span><\/p>\n

rho(lx,:)=1;    %\u51fa\u53e3<\/span>
\n u(lx,:)=u(lx-1,:);  v(lx,:)=v(lx-1,:);<\/span><\/p>\n

\n% \u83b7\u5f97\u6d78\u5165\u8fb9\u754c\u4e0a\u7684\u901f\u5ea6<\/span>
\n Ux=zeros(1,Nc);  Uy=zeros(1,Nc);<\/span>
\n for i=1:Nc<\/span>
\n      for j=floor(Xcy(i))-1:floor(Xcy(i))+2
\n          for k=floor(Ycy(i))-1:floor(Ycy(i))+2
\n<\/span>            rx=j-Xcy(i);  ry=k-Ycy(i);<\/span>
\n             Dx=1\/8*(3-2*abs(rx)+sqrt(1+4*abs(rx)-4*rx^2))*(abs(rx)<=1);<\/span>
\n             Dx=Dx+1\/8*(5-2*abs(rx)-sqrt(-7+12*abs(rx)-4*rx^2))*(abs(rx)<=2)*(abs(rx)>1);<\/span>
\n             Dy=1\/8*(3-2*abs(ry)+sqrt(1+4*abs(ry)-4*ry^2))*(abs(ry)<=1);<\/span>
\n             Dy=Dy+1\/8*(5-2*abs(ry)-sqrt(-7+12*abs(ry)-4*ry^2))*(abs(ry)<=2)*(abs(ry)>1);   <\/span>
\n             Ux(i)=Ux(i)+u(j,k)*Dx*Dy;   Uy(i)=Uy(i)+v(j,k)*Dx*Dy;<\/span>
\n          end<\/span>
\n      end<\/span>
\n end<\/span><\/p>\n

%\u8ba1\u7b97\u603b\u4f53\u79ef\u529b<\/span>
\n Uxi=Uxi+Ux;  Uyi=Uyi+Uy;<\/span>
\n Fx=-0.02*Uxi-2*Ux;   Fy=-0.02*Uyi-2*Uy;<\/span><\/p>\n

%\u6d78\u5165\u8fb9\u754c\u8ba1\u7b97\uff0c\u5c06L\u70b9n\u65f6\u523b\u4f53\u79ef\u529bspread\u5230n+1\u65f6\u523b\u7684Eular\u70b9\u4e0a\u53bb\u3002<\/span>
\n fx=zeros(lx,ly);  fy=zeros(lx,ly); <\/span>
\n %\u6e05\u7a7a\u4f53\u79ef\u529b\u5b58\u653e\u7a7a\u95f4<\/span>
\n for i=1:Ncfor i=1:Nc<\/span>
\n     for j=floor(Xcy(i))-1:floor(Xcy(i))+2
\n          for k=floor(Ycy(i))-1:floor(Ycy(i))+2
\n<\/span>            rx=j-Xcy(i);  ry=k-Ycy(i);<\/span><\/span><\/span>
\n             Dx=1\/8*(3-2*abs(rx)+sqrt(1+4*abs(rx)-4*rx^2))*(abs(rx)<=1);<\/span>
\n             Dx=Dx+1\/8*(5-2*abs(rx)-sqrt(-7+12*abs(rx)-4*rx^2))*(abs(rx)<=2)*(abs(rx)>1);<\/span>
\n             Dy=1\/8*(3-2*abs(ry)+sqrt(1+4*abs(ry)-4*ry^2))*(abs(ry)<=1);<\/span>
\n             Dy=Dy+1\/8*(5-2*abs(ry)-sqrt(-7+12*abs(ry)-4*ry^2))*(abs(ry)<=2)*(abs(ry)>1);   <\/span>
\n             fx(j,k)=fx(j,k)+Fx(i)*ds*Dx*Dy;  fy(j,k)=fy(j,k)+Fy(i)*ds*Dx*Dy;<\/span>
\n         end<\/span>
\n     end<\/span>
\n end<\/span><\/p>\n

%\u8ba1\u7b97\u5e73\u8861\u6001\u51fd\u6570
\nfor i=1:9
\n     M1=(ex(i)*u+ey(i)*v)\/cs^2;
\n     M2=M1.^2\/2;
\n     M3=(u.^2+v.^2)\/2\/cs^2;
\n     Feq(:,:,i)=rho.*W(i).*(1+M1+M2-M3);
\nend<\/p>\n

%\u78b0\u649e
\nfor i=1:9
\n    M1=3*(ex(i)-u).*fx+(ey(i)-v).*fy;
\n    M2=9*(ex(i)*u+ey(i)*v).*(ex(i).*fx+ey(i).*fy);
\n    force(:,:,i)=W(i)*(1-0.5\/(0.5+3*yu))*(M1+M2);
\nend
\n    F=F-1\/(0.5+3*yu)*(F-Feq)+force;
\n    
\n%\u5fae\u89c2\u8fb9\u754c\u8bbe\u7f6e
\n% F(BFin0)=F(BFin); %\u534a\u6b65\u53cd\u5f39\u64cd\u4f5c<\/span>
\nF(1,:,:)=Feq(1,:,:)+(F(2,:,:)-Feq(2,:,:));
\nF(lx,:,:)=Feq(lx,:,:)+(F(lx-1,:,:)-Feq(lx-1,:,:));
\nF(:,1,:)=Feq(:,1,:)+(F(:,2,:)-Feq(:,2,:));<\/span>
\n F(:,ly,:)=Feq(:,ly,:)+(F(:,ly-1,:)-Feq(:,ly-1,:));<\/span>
\n%\u540e\u5904\u7406<\/p>\n

if mod(tStep,100)==0
\nclc;clf
\ntStep
\nU=(u.^2+v.^2).^0.5;
\nsubplot(2,2,1),imagesc(U');<\/span>
\ncolormap jet
\nbox on
\naxis equal
\ncy=(ly-1)\/2;
\ny0=fx0\/2\/yu*(cy.^2-([0:ly-1]-cy).^2);
\nNi=floor(lx\/2);
\nsubplot(2,2,2),hold on,plot(y0,'k'),plot(u(Ni,:),'r'); hold off<\/span>
\nif tStep>1000<\/span>
\n Cd=[Cd,-sum(Fx*ds)\/(0.5*Uin^2*2*Rc)];  Cl=[Cl,-sum(Fy*ds)\/(0.5*Uin^2*2*Rc)];<\/span>
\n end<\/span>
\n subplot(2,2,3),plot(Cd,'b')<\/span>
\n subplot(2,2,4),plot(Cl,'b')<\/span>
\ndrawnow
\nend<\/p>\n

end  % \u4e3b\u5faa\u73af\u7ed3\u675f============================<\/p>\n","protected":false},"excerpt":{"rendered":"

[passster password=\"IB-LBM\" area=\"3212\"] %\u7ea2\u8272\u4ee3\u7801\u4e3a\u589e\u52a0\u4ee3\u7801\uff1b\u7eff\u5e95\u4e3a … \u7ee7\u7eed\u9605\u8bfb\u201c[LBM-4]\u5728\u53cd\u5f39\u8fb9\u754c\u5706\u67f1\u7ed5\u6d41\u57fa\u7840\u4e0a\u6539\u4e3aIB-LBM\u7248\u672c\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"views":1323,"_links":{"self":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts\/3167"}],"collection":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3167"}],"version-history":[{"count":6,"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts\/3167\/revisions"}],"predecessor-version":[{"id":3222,"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts\/3167\/revisions\/3222"}],"wp:attachment":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3167"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}