Problem with plotting 1D heat diffusion using FTCS

17 次查看（过去 30 天）
Giancarlo
Giancarlo 2024-3-9
评论： Torsten 2024-3-9
Ran in:
Hello, I have this issue with the plot where there is a sudden spike at the temperature near x and t are 0. I can't seem to find the problem with the code. The initial temperature is T(x,0) = x, and the ends of a 1m wire is insulated.
%FTCS march 9
clc;
clear;
c = 1; %alpha, thermal constant
L = 1; %wire length
T = 0.3; %total time
Nt = 6500; %time steps
Dt = T/Nt;
Nx = 100; %space steps
Dx = L/Nx;
b = c*Dt/(Dx*Dx); %must not exceed 1/2
fprintf ('b = %.2f \n', b);
b = 0.46
%Initial conditions
for i=1:Nx+1
x(i) = (i-1)*Dx;
u(i,1) = x(i);
end
%boundary Conditions
for k=1:Nt+1
u(1,k)= 0;
u(end,k)=0;
t(k)= (k-1)*Dt;
end
%FTCS
for k=1:Nt
for i=2:Nx
u(i,k+1) = u(i,k) + b.*(u(i-1,k)+u(i+1,k)-2.*u(i,k));
end
end
mesh(t,x,u)
title ('Plot of time and space')
xlabel('t')
ylabel('x')
zlabel('u')
  1 个评论
Torsten
Torsten 2024-3-9
If you start with
u(i,1) = x(i);
and set
u(1,k)= 0;
u(end,k)=0;
as boundary condition, there will be a discontinuity at x = 1.
Is it that what you mean ?

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