200 lines
No EOL
5.9 KiB
Matlab
200 lines
No EOL
5.9 KiB
Matlab
function [] = GetF2D()
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clear all
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% Define Main Solution Mesh
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NumX=10;
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NumY=10;
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delX=1.;
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delY=1.;
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for j=1:NumY+1
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for i=1:NumX+1
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index=i+(NumX+1)*(j-1);
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Node(index,1)=single((i-1.))*delX;
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Node(index,2)=single((j-1.))*delY;
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end
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end
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numNodes=(NumX+1)*(NumY+1);
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for j=1:NumY
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for i=1:NumX
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index=i+NumX*(j-1);
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Element(index,1)=i+(NumX+1)*(j-1);
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Element(index,2)=i+(NumX+1)*(j-1)+1;
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Element(index,3)=i+(NumX+1)*(j)+1;
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Element(index,4)=i+(NumX+1)*(j);
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end
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end
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numElem=(NumX)*(NumY);
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% Define Initial Level Set
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centx=5.;
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centy=5.;
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rad=2.5;
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for i=1:numNodes;
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dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
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lSet(i)=dist-rad;
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end
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% Plot initial level set
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[X,Y]=meshgrid(0:1.:10);
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Z=zeros(11);
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for i=1:numNodes
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Z(i)=lSet(i);
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end
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surf(X,Y,Z)
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% LS Algorithm Parameters
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bandwith=10.;
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% Loop through timesteps
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for tstep=1:1
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% Identify Narrow Band Elements
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NBindex=0;
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for i=1:numElem
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check=0;
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for iNd=1:4
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if abs(lSet(Element(i,iNd)))<=bandwidth*delX
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check=1;
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end
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end
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% If an element is in the narrow band split it into triangles
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if check==1
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NBindex=NBindex+1;
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NBelem(NBindex,1)=Element(i,1);
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NBelem(NBindex,2)=Element(i,2);
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NBelem(NBindex,3)=Element(i,3);
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NBindex=NBindex+1;
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NBelem(NBindex,1)=Element(i,1);
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NBelem(NBindex,2)=Element(i,3);
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NBelem(NBindex,3)=Element(i,4);
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end
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end
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% Velocity BC
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F=zeros(numNodes,1);
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for i=1:NBindex
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if lSet(NBelem(i,1))~=lSet(NBelem(i,2)) || lSet(NBelem(i,1))~=lSet(NBelem(i,3))
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F(NBelem(i,1))= 0.0005;
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F(NBelem(i,2))= 0.0005;
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F(NBelem(i,3))= 0.0005;
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end
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end
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% Assemble 'Stiffness' Matrices
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A=zeros(numNodes);
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for i=1:NBindex
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gpos=1/sqrt(3.);
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gx(1)=-gpos;
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gx(2)=gpos;
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gx(3)=gpos;
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gx(4)=-gpos;
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hx(1)=-gpos;
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hx(2)=-gpos;
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hx(3)=gpos;
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hx(4)=gpos;
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AfL=zeros(4);
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AfLGLS=zeros(4);
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for j=1:4
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g=gx(j);
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h=hx(j);
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phi(1)=0.25*(1.-g)*(1.-h);
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phi(2)=0.25*(1.+g)*(1.-h);
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phi(3)=0.25*(1.+g)*(1.+h);
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phi(4)=0.25*(1.-g)*(1.+h);
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phig(1)=0.25*-(1.-h);
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phig(2)=0.25*(1.-h);
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phig(3)=0.25*(1.+h);
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phig(4)=0.25*-(1.+h);
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rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
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dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
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AfL=AfL+(phi'*sign(rset))*(dls*phig);
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AfLGLS=AfLGLS+(phig'*dls)*(1./abs(dls))*(dls*phig);
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end
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for k=1:4;
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for j=1:4;
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A(Element(i,j),Element(i,k))=A(Element(i,j),Element(i,k))+AfL(j,k)+AfLGLS(j,k)
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end
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end
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end
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% Apply BCs
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RHS=zeros(numNodes,1);
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Sub=A*F;
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iindex=0;
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for i=1:numNodes
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if F(i)==0.
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iindex=iindex+1;
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RHSred(iindex)=RHS(i)-Sub(i);
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Fred=0.;
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jindex=0;
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for j=1:numNodes
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if F(j)==0.
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jindex=jindex+1;
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Ared(iindex,jindex)=A(i,j);
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end
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end
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end
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end
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% Solve for Fred
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Fred=(Ared^-1)*RHSred';
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% Get F
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iindex=0;
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for i=1:numNodes
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if F(i)==0.
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iindex=iindex+1;
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F(i)=Fred(iindex);
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end
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end
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% Update level set
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mMat=zeros(numNodes);
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mMatGLS=zeros(numNodes);
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f1=zeros(numNodes,1);
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f2=zeros(numNodes,1);
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f3=zeros(numNodes,1);
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h=1.;
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visc=0.000;
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for i=1:numElem
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gpos=1/sqrt(3.);
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gx(1)=-gpos;
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gx(2)=gpos;
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gx(3)=gpos;
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gx(4)=-gpos;
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hx(1)=-gpos;
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hx(2)=-gpos;
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hx(3)=gpos;
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hx(4)=gpos;
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mMatL=zeros(4);
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mMatGLSL=zeros(4);
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f1L=zeros(4,1);
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f2L=zeros(4,1);
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f3L=zeros(4,1);
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for j=1:4
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g=gx(j);
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h=hx(j);
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phi(1)=0.25*(1.-g)*(1.-h);
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phi(2)=0.25*(1.+g)*(1.-h);
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phi(3)=0.25*(1.+g)*(1.+h);
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phi(4)=0.25*(1.-g)*(1.+h);
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phig(1)=0.25*-(1.-h);
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phig(2)=0.25*(1.-h);
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phig(3)=0.25*(1.+h);
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phig(4)=0.25*-(1.+h);
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Floc=phi(1)*F(Element(i,1))+phi(2)*F(Element(i,2))+phi(3)*F(Element(i,3))+phi(4)*F(Element(i,4));
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rset=phi(1)*lSet(Element(i,1))+phi(2)*lSet(Element(i,2))+phi(3)*lSet(Element(i,3))+phi(4)*lSet(Element(i,4));
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dls=phig(1)*lSet(Element(i,1))+phig(2)*lSet(Element(i,2))+phig(3)*lSet(Element(i,3))+phig(4)*lSet(Element(i,4));
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mMatL=mMatL+phi'*phi;
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mMatGLSL=mMatGLSL+((phig'*(dls/abs(dls)))*Floc*(h/abs(Floc)))*phi;
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f1L=f1L+phi'*Floc*abs(dls);
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f2L=f2L+(phig'*(dls/abs(dls))*Floc)*(h/abs(Floc))*Floc*abs(dls);
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vs=h*((abs(visc+Floc*abs(dls)))/(abs(Floc*dls)+h));
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f3L=f3L+vs*phig'*dls;
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end
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for k=1:4;
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for j=1:4;
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mMat(Element(i,j),Element(i,k))=mMat(Element(i,j),Element(i,k))+mMatL(j,k);
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mMatGLS(Element(i,j),Element(i,k))=mMatGLS(Element(i,j),Element(i,k))+mMatGLSL(j,k);
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end
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f1(Element(i,k))=f1(Element(i,k))+f1L(k);
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f2(Element(i,k))=f2(Element(i,k))+f2L(k);
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f3(Element(i,k))=f3(Element(i,k))+f3L(k);
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end
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end
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dt=0.01;
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lSet=lSet-((((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3))';
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end
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%scatter3(Node(:,1), Node(:,2), lSet');
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