source: issm/trunk-jpl/test/NightlyRun/test1207.m

%Test Name: EISMINTRoundIceSheetStaticFS
%The aim of this program is to compare a model with an analytical solution given in SSA EISMINT : Lessons in Ice-Sheet Modeling.
printingflag=false;

numlayers=10;
resolution=30000.;

%To begin with the numerical model
md=model();
md=roundmesh(md,750000.,resolution);
md=setmask(md,'',''); %We can not test iceshelves nor ice rises with this analytical solution
md=parameterize(md,'../Par/RoundSheetStaticEISMINT.par');

%Calculation of the analytical 2d velocity field
constant=0.3;
vx_obs=constant/2.*md.mesh.x.*(md.geometry.thickness).^-1;
vy_obs=constant/2.*md.mesh.y.*(md.geometry.thickness).^-1;
vel_obs=sqrt((md.inversion.vx_obs).^2+(md.inversion.vy_obs).^2);

%We extrude the model to have a 3d model
md=extrude(md,numlayers,1.);
md=setflowequation(md,'FS','all');

%Spc the nodes on the bed
pos=find(md.mesh.vertexonbase);
md.stressbalance.spcvx(pos)=0.;
md.stressbalance.spcvy(pos)=0.;
md.stressbalance.spcvz(pos)=0.;

%Now we can solve the problem 
md.cluster=generic('name',oshostname(),'np',8);
md=solve(md,'Stressbalance');

%Calculate the depth averaged velocity field (2d):
vx=(md.results.StressbalanceSolution.Vx);
vy=(md.results.StressbalanceSolution.Vy);
vel=zeros(md.mesh.numberofvertices2d,1);

for i=1:md.mesh.numberofvertices2d
        node_vel=0.;
        for j=1:md.mesh.numberoflayers-1
                node_vel=node_vel+1./(2.*(md.mesh.numberoflayers-1))*...
                        (sqrt(vx(i+j*md.mesh.numberofvertices2d,1).^2+vy(i+j*md.mesh.numberofvertices2d,1).^2)+...
                        sqrt(vx(i+(j-1)*md.mesh.numberofvertices2d,1).^2+vy(i+(j-1)*md.mesh.numberofvertices2d,1).^2));
        end
        vel(i,1)=node_vel;
end

%Plot of the velocity from the exact and calculated solutions
figure(1)
subplot(2,2,1)
p=patch('Faces',md.mesh.elements2d,'Vertices',[md.mesh.x2d md.mesh.y2d],'FaceVertexCData',...
vel,'FaceColor','interp','EdgeColor','none');
title('Modelled velocity','FontSize',14,'FontWeight','bold')
colorbar; 
caxis([0 200]);
   
subplot(2,2,2)
p=patch('Faces',md.mesh.elements2d,'Vertices',[md.mesh.x2d md.mesh.y2d],'FaceVertexCData',...
vel_obs,'FaceColor','interp','EdgeColor','none');
title('Analytical velocity','FontSize',14,'FontWeight','bold')
colorbar; 
caxis([0 200]);

subplot(2,2,3)
hold on;
plot(sqrt((md.mesh.x(1:md.mesh.numberofvertices2d)).^2+(md.mesh.y(1:md.mesh.numberofvertices2d)).^2),vel,'r.');
plot(sqrt((md.mesh.x2d).^2+(md.mesh.y2d).^2),vel_obs,'b.');
title('Analytical vs calculated velocity','FontSize',14,'FontWeight','bold');
xlabel('distance to the center of the icesheet [m]','FontSize',14,'FontWeight','bold');
ylabel('velocity [m/yr]','FontSize',14,'FontWeight','bold');
legend('calculated velocity','exact velocity');
axis([0 750000 0 200]);
hold off;

subplot(2,2,4)
p=patch('Faces',md.mesh.elements2d,'Vertices',[md.mesh.x2d md.mesh.y2d],'FaceVertexCData',...
abs(vel-vel_obs)./vel_obs*100,'FaceColor','interp','EdgeColor','none');
title('Relative misfit [%]','FontSize',14,'FontWeight','bold')
colorbar;
caxis([0 100]);

if printingflag,
        set(gcf,'Color','w')
        printmodel('FSstatic','png','margin','on','marginsize',25,'frame','off','resolution',0.7,'hardcopy','off');
        system(['mv FSstatic.png ' ISSM_DIR '/website/doc_pdf/validation/Images/EISMINT/IceSheet']);
end

%Fields and tolerances to track changes
field_names     ={ ...
        'Vx','Vy','Vel', ...
};
field_tolerances={ ...
        1e-12,1e-12,1e-12, ...
};
field_values={ ...
        vx,vy,vel, ...
};