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fennecs/matlab/ForceBalance.m
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ForceBalance.m
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function ForceBalance(M,it,norm,log,contourscale, zlims)
%ForceBalance Show the radial force balance
% Plot the three radial forces for the given time-step it or averaged
% over the range of time steps defined in it
if it==':'
it=1:size(M.t2d);
end
switch nargin
case 2
contourscale=0.6;
norm=false;
log=false;
zlims=[-inf inf];
case 3
log=false;
contourscale=0.6;
zlims=[-inf inf];
case 4
contourscale=0.6;
zlims=[-inf inf];
case 5
zlims=[-inf inf];
case 6
otherwise
error("Invalid number of arguments")
end
r=(M.rgrid(1:end-1)+M.rgrid(2:end))/2;
z=(M.zgrid(1:end-1)+M.zgrid(2:end))/2;
[Zc,Rc]=meshgrid(z,r);
[Z,R]=meshgrid(M.zgrid,M.rgrid);
contourcolor=[0 0 0];%[255 20 147]/255;
avgpresstens=M.Presstens(:,1:end-1,1:end-1,it);
uThet=M.fluidUTHET(1:end-1,1:end-1,it);
Ntmp=M.N(1:end-1,1:end-1,it);
dim3=size(Ntmp,3);
presstens=zeros(6,size(M.rgrid,1),size(M.zgrid,1),dim3);
fluiduThet=zeros(size(M.rgrid,1),size(M.zgrid,1),dim3);
N=zeros(size(M.rgrid,1),size(M.zgrid,1),dim3);
for j=1:size(avgpresstens,4)
for i=1:6
presstens(i,:,:,j)=interp2(Zc,Rc,squeeze(avgpresstens(i,:,:,j)),Z,R);
end
fluiduThet(:,:,j)=interp2(Zc,Rc,uThet(:,:,j),Z,R);
N(:,:,j)=interp2(Zc,Rc,Ntmp(:,:,j),Z,R);
end
presstens(isnan(presstens))=0;
fluiduThet(isnan(fluiduThet))=0;
N(isnan(N))=0;
dr=[(M.rgrid(3)-M.rgrid(1))/2;(M.rgrid(3:end)-M.rgrid(1:end-2))/2];
dz=[(M.zgrid(3)-M.zgrid(1))/2;(M.zgrid(3:end)-M.zgrid(1:end-2))/2];
[dz, dr]=meshgrid(dz,dr);
Rinv=1./R;
%Rinv=padarray(Rinv, [1,1], 0, 'post');
Rinv(1,:)=0;
dpr=zeros(size(N,1)-1,size(N,2)-1,dim3);
dpz=zeros(size(N,1)-1,size(N,2)-1,dim3);
for j=1:size(presstens,4)
dpr(:,:,j)=squeeze(presstens(1,2:end,1:end-1,j)-presstens(1,1:end-1,1:end-1,j))./dr;
dpz(:,:,j)=squeeze(presstens(4,1:end-1,2:end,j)-presstens(4,1:end-1,1:end-1,j))./dz;
end
dpr=padarray(dpr, [1,1,0], 0, 'post');
dpz=padarray(dpz, [1,1,0], 0, 'post');
maxdens=max(N(:));
densitycontour=contour(M.zgrid,M.rgrid,mean(N,3),[contourscale contourscale]*maxdens);
Eforce=-M.qe*N.*M.Er(:,:,it);
Bforce=zeros(size(N,1),size(N,2),size(N,3));
inertforce=zeros(size(N,1),size(N,2),size(N,3));
Pressforce=zeros(size(N,1),size(N,2),size(N,3));
for j=1:size(N,3)
Bforce(:,:,j)=-M.qe*N(:,:,j).*fluiduThet(:,:,j).*M.Bz';
inertforce(:,:,j)=M.me*N(:,:,j).*fluiduThet(:,:,j).^2.*Rinv;
Pressforce(:,:,j)=-( dpr(:,:,j)...
+ squeeze(presstens(1,:,:,j)).*Rinv + squeeze(-presstens(4,:,:,j)).*Rinv...
+ dpz(:,:,j) );
end
Fmax=max([max(Eforce(:)),max(Bforce(:)),max(inertforce(:)),max(Pressforce(:))]);
if log
E=Eforce(Eforce~=0);
B=Bforce(Bforce~=0);
inert=inertforce(inertforce~=0);
press=Pressforce(Pressforce~=0);
Fmin=min([min(abs(E(:))),min(abs(B(:))),min(abs(inert(:))),min(abs(press(:)))]);
else
Fmin=min([min(Eforce(:)),min(Bforce(:)),min(inertforce(:)),min(Pressforce(:))]);
end
rgridmax=sum(M.nnr(1:2));
f=figure();
ax1=subplot(4,1,1);
plotvalue(ax1,mean(Eforce,3),'Electric force density', 'F_E [Nm^{-3}]',false);
%zlim=[Fmin Fmax];
zlim=[-inf inf];
ax2=subplot(4,1,2);
plotvalue(ax2,mean(Bforce,3),'Magnetic force density','F_B [Nm^{-3}]',false,zlim)
ax3=subplot(4,1,3);
plotvalue(ax3,mean(inertforce,3),'Centrifugal force density','F_i [Nm^{-3}]',false,zlim)
ax4=subplot(4,1,4);
plotvalue(ax4,mean(Pressforce,3),'Pressure force density','F_p [Nm^{-3}]',false,zlim)
linkaxes([ax1 ax2 ax3 ax4],'xy')
sgtitle(sprintf('Radial forces t=[%1.2g-%1.2g]s n_e=%1.2gm^{-3}',M.t2d(min(it)),M.t2d(max(it)),double(maxdens)))
f.PaperOrientation='portrait';
[~, name, ~] = fileparts(M.file);
f.PaperUnits='centimeters';
papsize=[20 29];
f.PaperSize=papsize;
print(f,sprintf('%sforce_balance',name),'-dpdf','-fillpage')
%% Radial relative forces
f=figure();
old_log=log;
log=true;
ax1=subplot(4,1,1);
plotvalue(ax1,mean(Eforce./Bforce,3),'Relative Electric force density', 'F_{Er}/F_{Br} [Nm^{-3}]',false);
%zlim=[Fmin Fmax];
zlim=[-inf inf];
ax2=subplot(4,1,2);
plotvalue(ax2,mean(Bforce./Bforce,3),'Relative Magnetic force density','F_{Br}/F_{Br} [Nm^{-3}]',false)
ax3=subplot(4,1,3);
plotvalue(ax3,mean(inertforce./Bforce,3),'Relative Centrifugal force density','F_i/F_{Br} [Nm^{-3}]',false)
ax4=subplot(4,1,4);
plotvalue(ax4,mean(Pressforce./inertforce,3),'Relative Pressure force density','F_{pr}/F_{Br} [Nm^{-3}]',false)
linkaxes([ax1 ax2 ax3 ax4],'xy')
sgtitle(sprintf('Relative radial forces t=[%1.2g-%1.2g]s n_e=%1.2gm^{-3}',M.t2d(min(it)),M.t2d(max(it)),double(maxdens)))
f.PaperOrientation='portrait';
[~, name, ~] = fileparts(M.file);
f.PaperUnits='centimeters';
papsize=[20 29];
f.PaperSize=papsize;
print(f,sprintf('%s_relatforce_balance',name),'-dpdf','-fillpage')
log=old_log;
f2=figure();
ax5=subplot(2,1,1);
totforce=mean(Eforce+Bforce+inertforce+Pressforce,3);
Forcemax=cat(3,mean(Eforce,3),mean(Bforce,3),mean(inertforce,3),mean(Pressforce,3));
Forcemax=max(Forcemax,[],3);
plotvalue(ax5,totforce./Forcemax,'Total force density','F [Nm^{-3}]',false,zlims)
ax6=subplot(2,1,2);
surface(ax6,M.zgrid,M.rgrid,mean(N,3),'edgecolor','none');
hold on;
zlevel=interp2(M.zgrid, M.rgrid, mean(N,3), densitycontour(1,2:end), densitycontour(2,2:end));
plot3(ax6,densitycontour(1,2:end),densitycontour(2,2:end),zlevel,'-.','linewidth',2,'color',contourcolor)
xlim(ax6,[M.zgrid(1) M.zgrid(end)])
ylim(ax6,[M.rgrid(1) M.rgrid(rgridmax)])
colormap(ax6,'parula')
xlabel(ax6,'z [m]')
ylabel(ax6,'r [m]')
title(ax6,'Density')
c = colorbar(ax6);
c.Label.String= 'n[m^{-3}]';
view(ax6,2)
sgtitle(sprintf('Radial forces sum t=[%1.2g-%1.2g]s n_e=%1.2g m^{-3}',M.t2d(min(it)),M.t2d(max(it)),double(maxdens)))
f2.PaperOrientation='portrait';
[~, name, ~] = fileparts(M.file);
f2.PaperUnits='centimeters';
papsize=[20 29];
f2.PaperSize=papsize;
print(f2,sprintf('%sforce_dens',name),'-dpdf','-fillpage')
f3=figure();
subN=M.N(:,:,it);
t=M.t2d(it);
UR=M.fluidUR(:,:,it);
UZ=M.fluidUZ(:,:,it);
dndt=zeros(size(subN,1)-1,size(subN,2)-1,size(subN,3)-1);
ndivu=zeros(size(subN,1)-1,size(subN,2)-1,size(subN,3)-1);
ugradn=zeros(size(subN,1)-1,size(subN,2)-1,size(subN,3)-1);
for i=1:size(subN,3)-1
dndt(:,:,i)=(subN(1:end-1,1:end-1,i+1)-subN(1:end-1,1:end-1,i))./(t(i+1)-t(i));
ndivu(:,:,i)=subN(1:end-1,1:end-1,i).*(UR(2:end,1:end-1,i)-UR(1:end-1,1:end-1,i))./dr...
+ UR(1:end-1,1:end-1,i).*subN(1:end-1,1:end-1,i)./Rc...
+ subN(1:end-1,1:end-1,i).*(UZ(1:end-1,2:end,i)-UZ(1:end-1,1:end-1,i))./dz;
ugradn(:,:,i)= UR(1:end-1,1:end-1,i).*(subN(2:end,1:end-1,i)-subN(1:end-1,1:end-1,i))./dr ...
+ UZ(1:end-1,1:end-1,i).*(subN(1:end-1,2:end,i)-subN(1:end-1,1:end-1,i))./dz;
end
dndt=padarray(dndt, [1,1], 0, 'post');
ndivu=padarray(ndivu, [1,1], 0, 'post');
ugradn=padarray(ugradn, [1,1], 0, 'post');
ax7=subplot(4,1,1);
plotvalue(ax7,mean(dndt,3),'\partialn/\partialt','\partialn/\partialt [m^{-3}s^{-1}]',true)
zlim=[max([min(min(mean(ndivu(2:end,:,:),3))),min(min(mean(ugradn(2:end,:,:),3)))]) min([max(max(mean(ndivu(2:end,:,:),3))),max(max(mean(ugradn(2:end,:,:),3)))])];
ax8=subplot(4,1,2);
plotvalue(ax8,mean(ndivu,3),'n\nabla(u)','n\nabla(u)[m^{-3}s^{-1}]',true,zlim)
ax9=subplot(4,1,3);
plotvalue(ax9,mean(ugradn,3),'u\nabla(n)','u\nabla(n)[m^{-3}s^{-1}]',true,zlim)
ax10=subplot(4,1,4);
plotvalue(ax10,mean(ndivu+ugradn+dndt,3),'Total','total[m^{-3}s^{-1}]',true,zlim)
sgtitle(sprintf('Continuity t=[%1.2g-%1.2g]s n_e=%1.2g m^{-3}',M.t2d(min(it)),M.t2d(max(it)),double(maxdens)))
f3.PaperOrientation='portrait';
[~, name, ~] = fileparts(M.file);
f3.PaperUnits='centimeters';
papsize=[20 19];
f3.PaperSize=papsize;
print(f3,sprintf('%scontinuity',name),'-dpdf','-fillpage')
function plotvalue(axis,matrix,titl, clab, rm1strow, zlims)
if nargin < 5
rm1strow=false;
end
if nargin>5
zmin=zlims(1);
zmax=zlims(2);
elseif log
zmin=0;
zmax=inf;
else
zmin=-inf;
zmax=inf;
end
if rm1strow
if log
h=surface(axis,M.zgrid,M.rgrid(2:end),abs(matrix(2:end,:)));
else
h=surface(axis,M.zgrid,M.rgrid(2:end),matrix(2:end,:));
end
else
if log
h=surface(axis,M.zgrid,M.rgrid,abs(matrix));
else
h=surface(axis,M.zgrid,M.rgrid,matrix);
end
end
set(h,'edgecolor','none');
hold on;
if log
zpos=interp2(M.zgrid, M.rgrid, abs(matrix), densitycontour(1,2:end), densitycontour(2,2:end));
else
zpos=interp2(M.zgrid, M.rgrid, matrix, densitycontour(1,2:end), densitycontour(2,2:end));
end
plot3(axis,densitycontour(1,2:end),densitycontour(2,2:end),zpos,'-.','linewidth',2,'color',contourcolor)
xlabel(axis,'z [m]')
ylabel(axis,'r [m]')
xlim(axis,[M.zgrid(1) M.zgrid(end)])
ylim(axis,[M.rgrid(1) M.rgrid(rgridmax)])
colormap(axis,'jet')
c = colorbar(axis);
c.Label.String=clab;
caxis(axis,[zmin zmax])
if norm
caxis(axis,[Fmin Fmax]);
end
if log
set(axis,'colorscale','log')
caxis(axis,'auto')
end
title(axis,titl)
grid(axis, 'on')
view(axis,2)
end
end
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