test_temperature.txt

% test for temperature discrete
% set R=10
% set phase field parameter equals to zero
% range temperature from 0.9 to 1.2
% test if the discrete euqation makes sense

clear;clc;clf;tic
nx=9;    
ny=nx;
dx=0.03;
xnode=dx:dx:nx;
r=length(xnode);
dy=dx;
ynode=dy:dy:ny;
s=length(ynode);
dt=0.0001;

R=10;
K=2.0;

P=zeros(r,s);
Pn=zeros(r,s);

T=zeros(r,s);
Tn=zeros(r,s);
Te=zeros(r,s);

for n=0.9:0.05:1.2
    n
    for i=1:r
    for j=1:s
        T(i,j)=0;  % T=Treal/Tm
        Te(i,j)=n;
        
        if (i-r/2)^2+(j-s/2)^2<R^2
            T(i,j)=1;

            
        end
        
    end
    end
end


 for i=1:r
    for j=1:s
    if i==1 && j==1
                Tn(i,j)=K*(Pn(i,j)-P(i,j))+T(i,j);
            elseif i==r && j==1
                Tn(i,j)=K*(Pn(i,j)-P(i,j))+T(i,j);
            elseif i==1 && j==s
                Tn(i,j)=K*(Pn(i,j)-P(i,j))+T(i,j);
            elseif i==r && j==s
                Tn(i,j)=K*(Pn(i,j)-P(i,j))+T(i,j);
            elseif i<r && i>1 && j==1
                Tn(i,j)=dt/(dx)^2*(T(i+1,j)+T(i-1,j)-2*T(i,j))+K*(Pn(i,j)-P(i,j))+T(i,j);
            elseif i<r && i>1 && j==s
                Tn(i,j)=dt/(dx)^2*(T(i+1,j)+T(i-1,j)-2*T(i,j))+K*(Pn(i,j)-P(i,j))+T(i,j);
            elseif j<r && j>1 && i==1
                Tn(i,j)=dt/(dy)^2*(T(i,j+1)+T(i,j-1)-2*T(i,j))+K*(Pn(i,j)-P(i,j))+T(i,j);
            elseif j<r && j>1 && i==r
                Tn(i,j)=dt/(dy)^2*(T(i,j+1)+T(i,j-1)-2*T(i,j))+K*(Pn(i,j)-P(i,j))+T(i,j);
           else
                 Tn(i,j)=dt*(T(i,j+1)+T(i,j-1)+T(i+1,j)+T(i-1,j)+0.5*(T(i+1,j+1)+T(i+1,j-1)+T(i-1,j+1)+T(i-1,j-1))-6*T(i,j))/(dx)^2+K*(Pn(i,j)-P(i,j))+T(i,j);
    end
    end
 end