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Solve_MAC.m
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Solve_MAC.m
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if ~isfield(display,'calculated') || ~isfield(display.calculated,'figure')
display.calculated.figure = figure();
if display.set_Figure_Position &&~ video.record
display.calculated.figure.Position=display.figure_Position;
end
else
if ~isgraphics(display.calculated.figure,'figure')
display.calculated.figure = figure();
if display.set_Figure_Position &&~ video.record
display.calculated.figure.Position=display.figure_Position;
end
end
end
lastwarn('')%clearing warnings...
time_step = 0;
pde.calculated.u0 = @(x,y) pde.u0t(x,y,0);
pde.calculated.v0 = @(x,y) pde.v0t(x,y,0);
pde.calculated.un = @(x,y) pde.unt(x,y,0);
pde.calculated.vn = @(x,y) pde.vnt(x,y,0);
pde.calculated.fu = @(x,y) pde.fut(x,y,0);
pde.calculated.fv = @(x,y) pde.fvt(x,y,0);
if pde.dynamic.dynamic && video.record
if display.full_HD_for_video
factor = 1+display.monitor_4k;
display.calculated.figure.Position = [(factor-1)*1920/4 (factor-1)*1088/4 1920/factor 1088/factor];
end
try
VideoObj = VideoWriter(video.name,video.profile);
VideoObj.FrameRate = video.FrameRate;
open(VideoObj);
catch ME
switch ME.identifier
case 'MATLAB:audiovideo:VideoWriter:fileNotWritable'
warning('Videofile was not writable. Trying to close it...')
close(VideoObj);
VideoObj = VideoWriter(video.name,video.profile);
VideoObj.FrameRate = video.FrameRate;
open(VideoObj);
disp('Successfully reopend the Videofile');
otherwise
rethrow(ME)
end
end
end
domain.calculated.on_domain = @(x,y) x>=0 & y>=0 & x<=domain.lx & y<=domain.ly &~domain.on_obstacle(x,y);
display.calculated.hx = domain.lx/display.nx;
display.calculated.hy = domain.ly/display.ny;
mesh.calculated = Generate_Mesh(domain,mesh,display);
%Compute System Matrix M:
UxU = Create_UxU_Block(mesh);
%figure();spy(UxU);
UxV = sparse(mesh.calculated.nu,mesh.calculated.nv);
UxP = Create_UxP_Block(mesh);
VxV = Create_VxV_Block(mesh);
%figure();spy(VxV);
VxP = Create_VxP_Block(mesh);
PxP = sparse(mesh.calculated.np,mesh.calculated.np);
M = [ UxU , UxV , UxP;
UxV', VxV , VxP;
UxP', VxP', PxP];
if(debugging.cleanup)
clear UxU UxV UxP VxV VxP PxP
end
%figure();spy(M);
%Apply Forces
F = sparse(mesh.calculated.DOFs,1);
F(1:mesh.calculated.nu) = pde.calculated.fu(mesh.calculated.X_u(:)',mesh.calculated.Y_u(:)');
F(mesh.calculated.nu+1:mesh.calculated.nu+mesh.calculated.nv) = pde.calculated.fv(mesh.calculated.X_v(:)',mesh.calculated.Y_v(:)');
[M,F] = Restrict_To_Domain(M,F,mesh.calculated.domain_vec);
[M,F] = Apply_BCs_U( M,F,domain,mesh,pde);
[M,F] = Apply_BCs_V( M,F,domain,mesh,pde);
for i=find(sum(M(1:mesh.calculated.nu+mesh.calculated.nv,mesh.calculated.nu+mesh.calculated.nv+(1:mesh.calculated.np))')~=0)
%find missing neighboring p's
M(i,mesh.calculated.nu+mesh.calculated.nv+(1:mesh.calculated.np))=0;
end
meanline = mesh.h^2*[zeros(1,mesh.calculated.nu+mesh.calculated.nv),ones(1,mesh.calculated.np)]; %a matrix line representing the pressure mean
if debugging.rankcheck
Mfull = full(M);
disp(['Rank of Mfull = ', num2str(rank(Mfull)), ' out of ', num2str(np+nu+nv),' DOFs'])
disp(['Rank of u submatrix = ', num2str(rank(Mfull(1:nu,1:nu))),' out of ', num2str(nu)])
disp(['Rank of v submatrix = ', num2str(rank(Mfull(nu+(1:nv),nu+(1:nv)))),' out of ', num2str(nv)])
if rank(Mfull) <nu+nv+np-1
return
end
end
if ~pde.dynamic.dynamic
u_sol = [M;meanline]\[F;0];
%u_sol = lsqminnorm([M;meanline],[F;0]);
% reordering
U = reshape(u_sol(1:mesh.calculated.nu),mesh.calculated.nx+1,mesh.calculated.ny)';
V = reshape(u_sol(mesh.calculated.nu+1:mesh.calculated.nu+mesh.calculated.nv),mesh.calculated.nx,mesh.calculated.ny+1)';
P = reshape(u_sol(mesh.calculated.nu+mesh.calculated.nv+1:end),mesh.calculated.nx,mesh.calculated.ny)';
%% Plotting routine
Plot_Solution; %TODO FUNCTION!
else
u_sol = zeros(mesh.calculated.DOFs,1);
u_start_matrix = pde.dynamic.u_start(mesh.calculated.X_u,mesh.calculated.Y_u);
u_sol(1:mesh.calculated.nu)=u_start_matrix(:);
v_start_matrix = pde.dynamic.v_start(mesh.calculated.X_v,mesh.calculated.Y_v);
u_sol(mesh.calculated.nu+(1:mesh.calculated.nv))=v_start_matrix(:);
u_sol(~mesh.calculated.domain_vec) = 0;
S = spdiags([ones(mesh.calculated.nu+mesh.calculated.nv,1);zeros(mesh.calculated.np,1)],0,mesh.calculated.DOFs,mesh.calculated.DOFs);
S(mesh.calculated.on_bndry_u,:) = 0;
S(mesh.calculated.on_bndry_v+mesh.calculated.nu,:)=0;
%u_stat = M\F;%stationary solution
%u_sol(nu+nv+(1:np))=u_stat(nu+nv+(1:np));
%P_Mat = M(1:nu+nv,nu+nv+(1:np));
%p = P_Mat\(F(1:nu+nv)-M(1:nu+nv,1:nu+nv)*u_sol(1:nu+nv));
%u_sol(nu+nv+(1:np))=p;
%u_sol(on_bndry_u) = u0(X_u(on_bndry_u),Y_u(on_bndry_u));
%u_sol(on_bndry_v+nu) =v0(X_v(on_bndry_v),Y_v(on_bndry_v));
integrator.calculated.dT = integrator.T/integrator.nT;
U = reshape(u_sol(1:mesh.calculated.nu),mesh.calculated.nx+1,mesh.calculated.ny)';
V = reshape(u_sol(mesh.calculated.nu+1:mesh.calculated.nu+mesh.calculated.nv),mesh.calculated.nx,mesh.calculated.ny+1)';
P = reshape(u_sol(mesh.calculated.nu+mesh.calculated.nv+1:end),mesh.calculated.nx,mesh.calculated.ny)';
Plot_Solution;
if video.record
frame = getframe(display.calculated.figure);
writeVideo(VideoObj, frame);
end
for time_step=1:integrator.nT
%u_sol = (dT*theta*M+speye(size(M)))\(u_sol + dT*theta*F+dT*(1-theta)*(F-M*u_sol));
%u_sol = u_sol+dT*(F-M*u_sol);%explizit euler
%u_sol = (dT*M+speye(size(M)))\(F+u_sol);%implizit euler
if pde.dynamic.time_Dependent
pde.calculated.fu = @(x,y) pde.fut(x,y,time_step*integrator.calculated.dT);
pde.calculated.fv = @(x,y) pde.fvt(x,y,time_step*integrator.calculated.dT);
F(1:mesh.calculated.nu) = pde.calculated.fu(mesh.calculated.X_u(:)',mesh.calculated.Y_u(:)');
F(mesh.calculated.nu+1:mesh.calculated.nu+mesh.calculated.nv) = pde.calculated.fv(mesh.calculated.X_v(:)',mesh.calculated.Y_v(:)');
pde.calculated.u0 = @(x,y) pde.u0t(x,y,time_step*integrator.calculated.dT);
pde.calculated.v0 = @(x,y) pde.v0t(x,y,time_step*integrator.calculated.dT);
[M,F] = Apply_BCs_U( M,F,domain,mesh,pde);
[M,F] = Apply_BCs_V( M,F,domain,mesh,pde);
end
u_sol = [(S+integrator.calculated.dT*integrator.theta*M);integrator.calculated.dT*integrator.theta*meanline]\...
[((S+integrator.calculated.dT*(1-integrator.theta)*M)*u_sol+integrator.calculated.dT*F);0];
if debugging.stop_video_on_rank_deficit
[~,warn] = lastwarn;
if strcmp(warn,'MATLAB:nearlySingularMatrix') || strcmp(warn,'MATLAB:rankDeficientMatrix')
warning('The time evolution Matrix is singular. In order to resume anyway, please set stop_video_on_rank_deficit to false')
break;
end
end
%u_sol(on_bndry_u) = u0(X_u(on_bndry_u),Y_u(on_bndry_u));
%u_sol(on_bndry_v+nu) =v0(X_v(on_bndry_v),Y_v(on_bndry_v));
%PLOTTING!!!
if ~mod(time_step,integrator.plot_every)
U = reshape(u_sol(1:mesh.calculated.nu),mesh.calculated.nx+1,mesh.calculated.ny)';
V = reshape(u_sol(mesh.calculated.nu+1:mesh.calculated.nu+mesh.calculated.nv),mesh.calculated.nx,mesh.calculated.ny+1)';
P = reshape(u_sol(mesh.calculated.nu+mesh.calculated.nv+1:end),mesh.calculated.nx,mesh.calculated.ny)';
Plot_Solution;
drawnow();
if video.record
frame = getframe(display.calculated.figure);
writeVideo(VideoObj, frame);
end
end
end
end
if pde.dynamic.dynamic && video.record
close(VideoObj);
end