% This file can be run to check that the advection-diffusion  is correctly modeled.
% There is u=v=0 and w=cst everywhere the only thermal boundary conditions are an imposed temperature
% at upper surface and an impose flux at its base.
% Just run this file in Matlab, with a properly setup Ice code. 

md=model;
md=mesh(md,'../Exp/Square.exp',100000);
md=geography(md,'','');
md=parameterize(md,'../Par/SquareThermal.par');
md=extrude(md,30,1);   %NB: the more one extrudes, the better (10-> relative~0.35%, 20->0.1%, 30->0.05%)
md=setelementstype(md,'Pattyn','all'); 

%Thermal boundary conditions
pos1=find(md.elementonbed);     md.spctemperature(md.elements(pos1,1:3),1)=1; md.spctemperature(md.elements(pos1,1:3),2)=10;
pos2=find(md.elementonsurface); md.spctemperature(md.elements(pos2,4:6),1)=1; md.spctemperature(md.elements(pos2,4:6),2)=0;
md.vz=0.1*ones(md.numberofgrids,1);
md.vel=sqrt( md.vx.^2+ md.vy.^2+ md.vz.^2);
md.pressure=zeros(md.numberofgrids,1);

%analytical results
%d2T/dz2-w*rho_ice*c/k*dT/dz=0   T(surface)=0  T(bed)=10   => T=A exp(alpha z)+B
alpha=0.1/md.yts*md.rho_ice*md.heatcapacity/md.thermalconductivity;   %alpha=w rho_ice c /k  and w=0.1m/an
A=10/(exp(alpha*(-1000))-1);    %A=T(bed)/(exp(alpha*bed)-1)  with bed=-1000 T(bed)=10
B=-A;
md.observed_temperature=A*exp(alpha*md.z)+B;

%modeled  results
md=solve(md,'analysis_type',ThermalSolutionEnum);

%plot results
comp_temp=zeros(md.numberofgrids,1);
comp_temp(md.results.ThermalSolution.Temperature.index)=md.results.ThermalSolution.Temperature.value;
relative=abs((comp_temp-md.observed_temperature)./md.observed_temperature)*100;
relative(find(comp_temp==md.observed_temperature))=0;
plotmodel(md,'data',comp_temp,'title','modeled temperature','data','observed_temperature','view',3,'title','analytical temperature','view',3,'data',comp_temp-md.observed_temperature,'title','absolute error','view',3,'data',relative,'title','relative error [%]','view',3)

%Fields and tolerances to track changes
field_names     ={'AdvectionTemperature'};
field_tolerances={1e-13};
field_values    ={comp_temp};