the code print -inf in TT matrix. Please anyone helps

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%Geometry definition
L=0.3; %Length of the The rectangular bar in meter
W=0.4; %Width of the The rectangular bar in meter
%Material properties
alpha=11.234E-05; %theraml diffusivity
% computional details
i_max=31; %max divisions in x-direction
j_max=41; %max divisions in y-direction
req_error=0.01; %total variation condition in temp
delta_t=1; %time step
delta_x=L/(i_max-1); %Divisons in x-direction
delta_y=W/(j_max-1); %Divisons in y-direction
d=alpha*delta_t/(delta_x)^2;%Defining stability condition
%Solution initializing
T=zeros(i_max,j_max);
% Boundary conditions
T(:,1)=40;
T(:,j_max)=10;
TT=T;
%processing
error_mag=1;
iterations=0;
while error_mag > req_error
for i=2:(i_max-1)
for j=(2:j_max-1)
TT(i,j)=T(i,j)+d*(T(i-1,j)+T(i+1,j)+T(i,j-1)+T(i,j+1)-4*T(i,j));
end
end
iterations=iterations+1;
error_mag = 0;
for i=2:(i_max-1)
for j=2:(j_max-1)
error_mag =error_mag +abs(T(i,j)-TT(i,j)); %defining the total variance to calcualte the difference in temperature from one time level to the next
error_track(iterations)= error_mag;
end
end
if rem(iterations,1000)==0
iterations
error_mag
end
T=TT;
end
%plottting the solution
solution_x=linspace(0,0.3,7);
solution_y=linspace(0,0.4,41);
T_final = T(1:5:i_max,:);
[X,Y] = meshgrid(solution_x,solution_y);
T_1_ss=T(11,:);
%figure(1);
%contourf(X,Y,T_final.')
%colorbar
%colormap(jet)
title('Steady state Solution of FTCS Explicit scheme ')
xlabel('L')
ylabel('W')
figure(2);
plot(solution_y,T_1_ss)
title('Steady stateSolution of FTCS Explicit scheme')
xlabel('Y')
ylabel('Temperature')

Answers (1)

Torsten
Torsten on 3 Dec 2022
Your value of 1 for delta_t violates the CFL condition for stability of the explicit Euler scheme.
Choose a value that satisfies CFL.

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