diff --git a/Functions/FPE.prj b/Functions/FPE.prj new file mode 100644 index 0000000..92c6696 --- /dev/null +++ b/Functions/FPE.prj @@ -0,0 +1,2 @@ + + diff --git a/Functions/Force_diff_xy.m b/Functions/Force_diff_xy.m new file mode 100644 index 0000000..5b651ef --- /dev/null +++ b/Functions/Force_diff_xy.m @@ -0,0 +1,13 @@ +function [f1,f2] = Force_diff_xy(x1,x2) + +%分化图景的动力对坐标矩阵的函数 + +a =1; +b=1; +S=0.5; +n=4; +k=1; +Sn = S^n; +f1 = a*x1.^n./(Sn+x1.^n) + b*S^n./(Sn+x2.^n)-k*x1; +f2 = a*x2.^n./(Sn+x2.^n) + b*S^n./(Sn+x1.^n)-k*x2; +end \ No newline at end of file diff --git a/Functions/Force_ring_xy.m b/Functions/Force_ring_xy.m new file mode 100644 index 0000000..bccd8b6 --- /dev/null +++ b/Functions/Force_ring_xy.m @@ -0,0 +1,11 @@ +function [f1,f2] = Force_ring_xy(X,Y) +%环流动力-坐标juzhen函数 X Y分别为网格的横纵坐标矩阵 +a = 0.1; +b = 0.1; +c = 100; +eps = 0.1; +tau = 5; +f1 = (eps^2+X.^2)./((1+X.^2).*(1+Y))-a*X; +f2 = (b-Y./(1+c*X.^2))/tau; +end + diff --git a/Functions/deri_x1.m b/Functions/deri_x1.m new file mode 100644 index 0000000..edd6bd4 --- /dev/null +++ b/Functions/deri_x1.m @@ -0,0 +1,48 @@ +function [M] = deri_x1(L,Nx,D,bc,f) +%Force = ring +x = linspace(0,L,Nx); +dx = x(2)-x(1); + +%DERI_X x方向一阶导数 +N = Nx^2; +M = zeros(N,N); + +%内点 +for i= 2:Nx-1 + for j = 2:Nx-1 + n = Nx*(i-1); + M(n+j,n+j+1)=1/2; + M(n+j,n+j-1)=-1/2; + end +end +M = M/dx; + + +%left and right +for i = 1:Nx + [f1,f2]=Force_ring_xy(0,(i-1)*dx); + M((i-1)*Nx+1,(i-1)*Nx+1) = f1/D; + [f1,f2]=Force_ring_xy(L,(i-1)*dx); + M(i*Nx, i*Nx) = f1/D; +end + +if bc == 1 + n=Nx*(Nx-1); + for j=2:Nx-1 + [f1,f2]=Force_ring_xy((j-1)*dx,0); + M(j,j)=f1/D; + [f1,f2]=Force_ring_xy((j-1)*dx,L); + M(n+j,n+j)=f1/D; + end +else + for j=2:Nx-1 + M(j,j-1)=-1/(2*dx); + M(j,j+1)=1/(2*dx); + M(n+j,n+j-1)=-1/(2*dx); + M(n+j,n+j+1)=1/(2*dx); + end + + + +end +end diff --git a/Functions/grid-laplace.asv b/Functions/grid-laplace.asv new file mode 100644 index 0000000..434eef6 --- /dev/null +++ b/Functions/grid-laplace.asv @@ -0,0 +1,32 @@ +function [A] = grid-laplace(L,Nx) +%GRID-LAPLACE 均匀正方网格拉普拉斯算子 +%Grid +x=linspace(0,L,Nx); +dx = x(2)- x(1); + +%initialize Matrices + N = Nx^2; + M = zeros(N,N) + + + %内点 + for i =2:Nx-1 + for j = 2:Nx-1 + n=i+(j-1)*Nx; + M(n,n) = -4; + M(n,n-1) = 1; + M(n,n+1) = 1; + M(n,n-Nx) = 1; + M(n,n+Nx) = 1; + end + end + + %up + for j = 2:Nx-1 + + + + + +end + diff --git a/Functions/grid_laplace.m b/Functions/grid_laplace.m new file mode 100644 index 0000000..bec45a1 --- /dev/null +++ b/Functions/grid_laplace.m @@ -0,0 +1,126 @@ +function [M] = grid_laplace(L,Nx,BC,D) +%GRID-LAPLACE 均匀正方网格拉普拉斯算子 +x = linspace(0,L,Nx); +dx = x(2)-x(1); + + +%initialize Matrices + N = Nx^2; + M = zeros(N,N); + + + %内点 + for i =2:Nx-1 + for j = 2:Nx-1 + n=i+(j-1)*Nx; + M(n,n) = -4; + M(n,n-1) = 1; + M(n,n+1) = 1; + M(n,n-Nx) = 1; + M(n,n+Nx) = 1; + end + end + + + + + %down and up 内点 + n = (Nx-1)*Nx; + for j = 2:Nx-1 + M(j,j) = -2; + M(j,j-1)=1; + M(j,j+1)=1; + M(n+j,n+j)=-2; + M(n+j,n+j-1)=1; + M(n+j,n+j+1)=1; + + end + + %left and Right 内点 + for i = 2:Nx-1 + M(Nx*(i-1)+1,Nx*(i-1)+1)=-2; + M(Nx*(i-1)+1,Nx*(i-2)+1)=1; + M(Nx*(i-1)+1,Nx*i+1)=1; + M(Nx*i,Nx*i)=-2; + M(Nx*i,Nx*(i-1))=1; + M(Nx*i,Nx*(i+1))=1; + end + + + + %down and up 内点 + for j = 2:Nx-1 + [f1,f2] = Force_ring_xy(x(j),0); + M(j,j) = -2*f2*dx/D-2; + M(j,j+Nx) = 2; + [f1,f2] = Force_ring_xy(x(j),L); + M(n+j,n+j)=2*f2*dx/D+2; + M(n+j,n+j-Nx)=-2; + end + + %left and Right 内点 + for i = 2:Nx-1 + [f1,f2] = Force_ring_xy(0,x(i)); + M(Nx*(i-1)+1,Nx*(i-1)+1)=-2*f1*dx/D-2; + M(Nx*(i-1)+1,Nx*(i-1)+2)=2; + [f1,f2] = Force_ring_xy(L,x(i)); + M(Nx*i,Nx*i)=2*f1*dx/D+2; + M(Nx*i,Nx*i-1)=-2; + end + + %corner + %左上 + [f1,f2] = Force_ring_xy(0,L); + n=Nx*(Nx-1); + M(n+1,n+1) = 2*(f2-f1)*D*dx -4; + M(n+1,n-Nx+1) = 2; + M(n+1,n+2)=2; + + %右上 + [f1,f2] = Force_ring_xy(L,L); + n = Nx^2; + M(n,n) = 2*dx*(f1+f2)/D-4; + M(n,n-1)=2; + M(n,n-Nx)=2; + + %左下 + [f1,f2] = Force_ring_xy(0,0); + M(1,1)=-4-2*dx*(f1+f2)/D; + M(1,2)=2; + M(1,1+Nx)=2; + + %右下 + [f1,f2] = Force_ring_xy(L,0); + M(Nx,Nx) = 2*(f1-f2)*dx/D-4; + M(Nx,Nx-1)=2; + M(Nx,2*Nx)=2; + + + + + + if BC == 0 %Dirichlet边界 J=0 + %up and down 内点 + n = (Nx-1)*Nx; + for j = 2:Nx-1 + + + end + + %left and Right 内点 + for i = 2:Nx-1 + + end + + + + + + + + + + +end + + diff --git a/Functions/main.m b/Functions/main.m new file mode 100644 index 0000000..023cdf2 --- /dev/null +++ b/Functions/main.m @@ -0,0 +1,70 @@ +Lx = 4; +Ly = 4; +Nx = 100; +Ny = 100; +m = createMesh2D(Nx,Ny,Lx,Ly); + + +%边界 +D_val = 0.005; %diffusion coeeficient +BC = createBC(m); % all Neumann boundary condition structure +a = BC.left.a; +BC.left.a = -D_val*a; +BC.right.a = -D_val*a; +BC.top.a = -D_val*a; +BC.bottom.a = -D_val*a; + +[xb,yb] = Force_diff_xy(0,m.cellcenters.y); %diff/ring +BC.left.b = transpose(xb); +[xb,yb] = Force_diff_xy(Lx,m.cellcenters.y); +BC.right.b = transpose(xb); + +[xb,yb] = Force_diff_xy(m.cellcenters.x,0); +BC.bottom.b = transpose(yb); +[xb,yb] = Force_diff_xy(m.cellcenters.x,Ly); +BC.top.b = transpose(yb); + +c = 0.01*ones(1,Nx); +BC.left.c = -c; +BC.right.c = c; +BC.top.c = c; +BC.bottom.c = -c; + +%diffussion term +D = createCellVariable(m, D_val); % assign dif. coef. to all the cells +Dave = harmonicMean(D); % convert a cell variable to face variable + +%convection term +u_face = createFaceVariable(m, 1); % assign velocity value to cell faces +[x,y] = ndgrid(m.facecenters.x, m.cellcenters.y); +[xv,yv] = Force_diff_xy(x,y); +u_face.xvalue = xv; + +[x,y] = ndgrid(m.cellcenters.x, m.facecenters.y) +[xv,yv] = Force_diff_xy(x,y); +u_face.yvalue = yv; + +%solve +Mconv = convectionTerm(u_face); % convection term, central, second order +Mdiff = diffusionTerm(Dave); % diffusion term +[Mbc, RHS] = boundaryCondition(BC); % boundary condition discretization +M = Mconv-Mdiff+Mbc; % matrix of coefficient for central scheme +c = solvePDE(m, M, RHS); % solve for the central scheme +c.value = c.value-min(min(c.value)); +c.value = log(c.value); +%c.value = +visualizeCells2D(c); + + + + + + + + + + + + + + diff --git a/Functions/mainfunc.mlx b/Functions/mainfunc.mlx new file mode 100644 index 0000000..9ff5db8 Binary files /dev/null and b/Functions/mainfunc.mlx differ diff --git a/Functions/resources/project/EEtUlUb-dLAdf0KpMVivaUlztwA/fMVdNXBE2QxYwW97LIvhwXs6zQod.xml b/Functions/resources/project/EEtUlUb-dLAdf0KpMVivaUlztwA/fMVdNXBE2QxYwW97LIvhwXs6zQod.xml new file mode 100644 index 0000000..59b7a5d --- /dev/null +++ b/Functions/resources/project/EEtUlUb-dLAdf0KpMVivaUlztwA/fMVdNXBE2QxYwW97LIvhwXs6zQod.xml @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/Functions/resources/project/EEtUlUb-dLAdf0KpMVivaUlztwA/fMVdNXBE2QxYwW97LIvhwXs6zQop.xml b/Functions/resources/project/EEtUlUb-dLAdf0KpMVivaUlztwA/fMVdNXBE2QxYwW97LIvhwXs6zQop.xml new file mode 100644 index 0000000..4b4fc80 --- /dev/null +++ b/Functions/resources/project/EEtUlUb-dLAdf0KpMVivaUlztwA/fMVdNXBE2QxYwW97LIvhwXs6zQop.xml @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/Functions/resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/2kj09UetkV_lru3gvSPXnY6-nM4d.xml b/Functions/resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/2kj09UetkV_lru3gvSPXnY6-nM4d.xml new file mode 100644 index 0000000..f8fc820 --- /dev/null +++ b/Functions/resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/2kj09UetkV_lru3gvSPXnY6-nM4d.xml @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/Functions/resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/2kj09UetkV_lru3gvSPXnY6-nM4p.xml b/Functions/resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/2kj09UetkV_lru3gvSPXnY6-nM4p.xml new file mode 100644 index 0000000..7d7cdf5 --- /dev/null +++ b/Functions/resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/2kj09UetkV_lru3gvSPXnY6-nM4p.xml @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git 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newline at end of file diff --git a/Functions/resources/project/fjRQtWiSIy7hIlj-Kmk87M7s21k/NjSPEMsIuLUyIpr2u1Js5bVPsOsd.xml b/Functions/resources/project/fjRQtWiSIy7hIlj-Kmk87M7s21k/NjSPEMsIuLUyIpr2u1Js5bVPsOsd.xml new file mode 100644 index 0000000..1fba42f --- /dev/null +++ b/Functions/resources/project/fjRQtWiSIy7hIlj-Kmk87M7s21k/NjSPEMsIuLUyIpr2u1Js5bVPsOsd.xml @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/Functions/resources/project/fjRQtWiSIy7hIlj-Kmk87M7s21k/NjSPEMsIuLUyIpr2u1Js5bVPsOsp.xml b/Functions/resources/project/fjRQtWiSIy7hIlj-Kmk87M7s21k/NjSPEMsIuLUyIpr2u1Js5bVPsOsp.xml new file mode 100644 index 0000000..c9f987f --- /dev/null +++ b/Functions/resources/project/fjRQtWiSIy7hIlj-Kmk87M7s21k/NjSPEMsIuLUyIpr2u1Js5bVPsOsp.xml @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/Functions/resources/project/qaw0eS1zuuY1ar9TdPn1GMfrjbQ/AU57kxAjJtOFVtmwUqEp7goA-j8d.xml 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No newline at end of file diff --git a/Functions/resources/project/uuid-6d64d59a-434d-4b12-9691-31d0a86f1001.xml b/Functions/resources/project/uuid-6d64d59a-434d-4b12-9691-31d0a86f1001.xml new file mode 100644 index 0000000..1c0844e --- /dev/null +++ b/Functions/resources/project/uuid-6d64d59a-434d-4b12-9691-31d0a86f1001.xml @@ -0,0 +1,2 @@ + + \ No newline at end of file