{"id":3194,"date":"2024-02-14T21:20:42","date_gmt":"2024-02-14T13:20:42","guid":{"rendered":"http:\/\/81.70.49.155\/?p=3194"},"modified":"2024-02-14T21:20:42","modified_gmt":"2024-02-14T13:20:42","slug":"%e4%bb%8e%e5%8d%95%e7%9b%b8%e6%b5%81%ef%bc%88%e9%80%9a%e9%81%93%e6%b5%81%e5%8a%a8%ef%bc%89%e6%94%b9%e4%b8%ba%e5%a4%9a%e7%9b%b8%e6%b5%81%ef%bc%88shanchen-model%ef%bc%89-step1","status":"publish","type":"post","link":"http:\/\/81.70.49.155\/?p=3194","title":{"rendered":"\u4ece\u5355\u76f8\u6d41\uff08\u901a\u9053\u6d41\u52a8\uff09\u6539\u4e3a\u591a\u76f8\u6d41\uff08Shan&Chen model\uff09-Step1"},"content":{"rendered":"

\n\tStep1 \u8fd9\u4e00\u6b65\u5c06\u4e00\u4e9b\u6a21\u5757\u5355\u72ec\u62ff\u51fa\u6765\u505a\u5916\u6302\u5b50\u7a0b\u5e8f\uff0c\u8fd9\u4e9b\u5b50\u7a0b\u5e8f\u662f\u9700\u8981\u8fdb\u884c\u590d\u7528\u7684\uff0c\u8fd9\u8981\u505a\u53ef\u4ee5\u7b80\u5316\u4e3b\u7a0b\u5e8f\u3002
\n<\/h4>\n
\n\t\n<\/p>\n
\n\t%\u7ea2\u8272\u4ee3\u7801\u4e3a\u589e\u52a0\u4ee3\u7801\uff1b\u7eff\u5e95\u4e3a\u5c4f\u853d\u7684\u4ee3\u7801\n<\/p>\n
\n%\u521d\u59cb\u5316<\/p>\n
clc; clear; close;
\nlx=40; ly=20;
\nRe=1.25;
\nyu=0.1;
\nfx0=Re8yu^2\/(ly-1)^3;
\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);
\nopposite=[1,4,5,2,3,8,9,6,7];
\nrho=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; F0=F;<\/span><\/p>\n
%% \u4e3b\u5faa\u73af===========================================
\nfor tStep=1:20000
\nF=Stream(F,F0,lx,ly);<\/span><\/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)=rho(:,2);
\nrho(:,ly)=rho(:,ly-1);
\nu(:,1)=0; u(:,ly)=0;
\nv(:,1)=0; v(:,ly)=0;<\/p>\n
Feq=Feqf(rho,u,v,ex,ey,W,cs);<\/span><\/p>\n
%\u78b0\u649e
\nforce=Calforce(u,v,fx,fy,ex,ey,W,yu);<\/span>
\nF=F-1\/(0.5+3yu)(F-Feq)+force;
\n
\n%\u5fae\u89c2\u8fb9\u754c\u8bbe\u7f6e
\nF(:,[1,ly],:)=F(:,[1,ly],opposite);
\n% F(:,1,:)=Feq(:,1,:)+(F(:,2,:)-Feq(:,2,:));
\n% F(:,ly,:)=Feq(:,ly,:)+(F(:,ly-1,:)-Feq(:,ly-1,:));<\/p>\n
%\u540e\u5904\u7406
\nif mod(tStep,500)==0
\nclc;clf
\ntStep
\nU=(u.^2+v.^2).^0.5;
\nsubplot(1,2,1),imagesc(U');
\ncolormap jet
\naxis equal
\ncy=(ly-1)\/2;
\ny0=fx0\/2\/yu(cy.^2-([0:ly-1]-cy).^2);
\nNi=floor(lx\/2);
\nsubplot(1,2,2),hold on,plot(y0,'k'),plot(u(Ni,:),'r'); hold off
\ndrawnow
\nend<\/p>\n
\n\tend % \u4e3b\u5faa\u73af\u7ed3\u675f============================\n<\/p>\n
\n\t\n<\/p>\n
\n\t%%%%y\u4ee5\u4e0b\u4e3a\u5b50\u7a0b\u5e8f%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n<\/p>\n
\n\t%1 Stream.m \u8fc1\u79fb\uff01<\/span>\n<\/p>\n
\n\t\n<\/p>\n
\n\tfunction F=Stream(F,F0,lx,ly)<\/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
% \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;\n<\/p>\n
\n\t\n<\/p>\n
\n\t%2 Feqf.m \u8ba1\u7b97\u5e73\u8861\u6001\u5206\u5e03\u51fd\u6570<\/span>\n<\/p>\n
\n\t%function Feq=Feqf(rho,u,v,ex,ey,W,cs);
\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
%3 <\/span>Calforce.m \u8ba1\u7b97\u5916\u529b\u683c\u5f0f\uff08\u78b0\u649e\u90e8\u5206\u4f7f\u7528\uff09<\/span>\n<\/p>\n
\n\tfunction force=Calforce(u,v,fx,fy,ex,ey,W,yu)
\nfor i=1:9
\n M1=3(ex(i)-u).fx+3(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+3yu))*(M1+M2);
\nend<\/p>\n","protected":false},"excerpt":{"rendered":"
Step1 \u8fd9\u4e00\u6b65\u5c06\u4e00\u4e9b\u6a21\u5757\u5355\u72ec\u62ff\u51fa\u6765\u505a\u5916\u6302\u5b50\u7a0b\u5e8f\uff0c\u8fd9\u4e9b\u5b50\u7a0b\u5e8f\u662f\u9700\u8981\u8fdb\u884c\u590d\u7528\u7684\uff0c\u8fd9\u8981\u505a\u53ef\u4ee5\u7b80\u5316\u4e3b\u7a0b\u5e8f\u3002 %\u7ea2\u8272 … \u7ee7\u7eed\u9605\u8bfb\u201c\u4ece\u5355\u76f8\u6d41\uff08\u901a\u9053\u6d41\u52a8\uff09\u6539\u4e3a\u591a\u76f8\u6d41\uff08Shan&Chen model\uff09-Step1\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":782,"_links":{"self":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts\/3194"}],"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=3194"}],"version-history":[{"count":1,"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts\/3194\/revisions"}],"predecessor-version":[{"id":3195,"href":"http:\/\/81.70.49.155\/index.php?rest_route=\/wp\/v2\/posts\/3194\/revisions\/3195"}],"wp:attachment":[{"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3194"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3194"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/81.70.49.155\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}