How to implement mesh diagram?

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Deck Zhan Sim
Deck Zhan Sim 2021-1-20
评论： Deck Zhan Sim 2021-1-20
How to do the mesh diagram in this coding with the corresponding of T,L and time?
Below here are my codes:
clc;
clear all;
L=20;
alpha=0.23;
t_final=60;
n=20;
T0=20;
T1s=100;
T2s=0;
dx=L/n;
dt=2;
x=dx/2:dx:L-dx/2;
T=ones(n,1)*T0;
dTdt=zeros(n,1);
t=0:dt:t_final;
for j=1:length(t)
for i=2:n-1
dTdt(i)=alpha*(T(i+1)+T(i-1)-2*T(i))/dx^2;
end
dTdt(1)=alpha*(T(2)+T1s-2*T(1))/dx^2;
dTdt(n)=alpha*(T2s+T(n-1)-2*T(n))/dx^2;
T=T+dTdt*dt;
end
disp(T)
figure(1)
plot(x,T,'Linewidth',3)
axis([0 L 0 50])
xlabel('Distance(m)')
ylabel('Temperature(\circC)')

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回答（1 个）

Walter Roberson
Walter Roberson 2021-1-20
Ran in:
L=20;
alpha=0.23;
t_final=60;
n=20;
T0=20;
T1s=100;
T2s=0;
dx=L/n;
dt=2;
x=dx/2:dx:L-dx/2;
t = 0:dt:t_final;
nt = length(t);
T = zeros(n, nt);
T(:,1) = T0;
for j=1:nt-1
dTdt=zeros(n,1);
for i=2:n-1
dTdt(i) = alpha*(T(i+1,j)+T(i-1,j)-2*T(i,j))/dx^2;
end
dTdt(1) = alpha*(T(2,j)+T1s-2*T(1,j))/dx^2;
dTdt(n) = alpha*(T2s+T(n-1,j)-2*T(n,j))/dx^2;
T(:,j+1) = T(:,j) + dTdt*dt;
end
disp(T)
Columns 1 through 17 20.0000 56.8000 59.7440 67.7664 69.6541 73.2500 74.6082 76.6726 77.7084 79.0632 79.8832 80.8515 81.5184 82.2527 82.8066 83.3881 83.8561 20.0000 20.0000 36.9280 39.6365 47.1254 49.4526 53.7042 55.5970 58.3620 59.9089 61.8713 63.1527 64.6331 65.7095 66.8773 67.7936 68.7463 20.0000 20.0000 20.0000 27.7869 29.6557 34.8979 36.9150 40.5322 42.3785 45.0208 46.6451 48.6722 50.0879 51.7051 52.9399 54.2702 55.3525 20.0000 20.0000 20.0000 20.0000 23.5820 24.7282 27.9892 29.4811 32.1391 33.6637 35.8257 37.2693 39.0583 40.3851 41.8945 43.0996 44.3958 20.0000 20.0000 20.0000 20.0000 20.0000 21.6477 22.3068 24.2082 25.2140 27.0066 28.1446 29.7555 30.9131 32.3464 33.4688 34.7467 35.8096 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.7579 21.1218 22.1859 22.8235 23.9654 24.7582 25.8837 26.7478 27.8212 28.7044 29.7143 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.3487 20.5439 21.1228 21.5096 22.2077 22.7327 23.4828 24.0936 24.8575 25.5144 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.1604 20.2630 20.5715 20.7985 21.2122 21.5457 22.0267 22.4386 22.9586 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0738 20.1269 20.2886 20.4167 20.6542 20.8551 21.1502 21.4118 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0339 20.0572 20.1375 20.1995 20.3251 20.4304 20.5951 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 19.9915 20.0003 19.9931 20.0179 20.0241 20.0686 20.0961 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 19.9816 19.9683 19.9278 19.9026 19.8496 19.8199 19.7665 19.7401 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 19.9599 19.9342 19.8571 19.8004 19.6969 19.6167 19.4997 19.4070 19.2879 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 19.9128 19.8640 19.7193 19.6226 19.4481 19.3168 19.1293 18.9780 18.7886 18.6296 20.0000 20.0000 20.0000 20.0000 20.0000 20.0000 19.8105 19.7196 19.4535 19.2941 19.0086 18.8105 18.5291 18.3131 18.0447 17.8245 17.5729 20.0000 20.0000 20.0000 20.0000 20.0000 19.5881 19.4233 18.9479 18.6965 18.2483 17.9638 17.5611 17.2717 16.9134 16.6328 16.3133 16.0479 20.0000 20.0000 20.0000 20.0000 19.1045 18.8180 18.0027 17.6297 16.9652 16.5841 16.0436 15.6827 15.2354 14.9037 14.5264 14.2251 13.9011 20.0000 20.0000 20.0000 18.0533 17.5861 16.2755 15.7713 14.8670 14.4054 13.7448 13.3387 12.8319 12.4780 12.0737 11.7650 11.4324 11.1619 20.0000 20.0000 15.7680 15.0909 13.2186 12.6369 11.5739 11.1008 10.4095 10.0228 9.5322 9.2118 8.8417 8.5726 8.2807 8.0516 7.8134 20.0000 10.8000 10.0640 8.0584 7.5865 6.6875 6.3480 5.8318 5.5729 5.2342 5.0292 4.7871 4.6204 4.4368 4.2983 4.1530 4.0360 Columns 18 through 31 84.3318 84.7329 85.1320 85.4801 85.8214 86.1267 86.4234 86.6937 86.9548 87.1960 87.4283 87.6451 87.8535 88.0495 69.5357 70.3333 71.0207 71.7022 72.3066 72.8984 73.4344 73.9551 74.4340 74.8970 75.3278 75.7432 76.1331 76.5085 56.4736 57.4279 58.3910 59.2382 60.0784 60.8352 61.5773 62.2576 62.9197 63.5346 64.1304 64.6890 65.2289 65.7387 45.4862 46.6162 47.6030 48.6006 49.4954 50.3852 51.1991 51.9996 52.7422 53.4674 54.1473 54.8084 55.4329 56.0384 36.9554 37.9497 38.9837 39.9083 40.8469 41.7045 42.5610 43.3559 44.1413 44.8782 45.6013 46.2853 46.9533 47.5891 30.5862 31.5309 32.3744 33.2564 34.0627 34.8858 35.6509 36.4195 37.1425 37.8608 38.5423 39.2143 39.8559 40.4855 26.2707 26.9457 27.6825 28.3572 29.0679 29.7305 30.4117 31.0549 31.7053 32.3248 32.9443 33.5381 34.1272 34.6944 23.4227 23.9623 24.4574 25.0030 25.5135 26.0561 26.5706 27.1042 27.6149 28.1356 28.6372 29.1425 29.6316 30.1202 21.7477 22.0552 22.4184 22.7586 23.1386 23.5003 23.8894 24.2638 24.6564 25.0368 25.4286 25.8102 26.1981 26.5773 20.7412 20.9377 21.1189 21.3403 21.5499 21.7905 22.0221 22.2768 22.5249 22.7897 23.0495 23.3212 23.5889 23.8646 20.1619 20.2140 20.3008 20.3777 20.4842 20.5842 20.7085 20.8291 20.9691 21.1074 21.2610 21.4141 21.5791 21.7444 19.6958 19.6790 19.6499 19.6465 19.6360 19.6482 19.6571 19.6858 19.7140 19.7589 19.8052 19.8657 19.9287 20.0034 19.1931 19.0808 18.9917 18.8924 18.8144 18.7316 18.6680 18.6037 18.5565 18.5111 18.4809 18.4542 18.4408 18.4321 18.4463 18.2890 18.1175 17.9686 17.8128 17.6769 17.5391 17.4189 17.3004 17.1976 17.0986 17.0136 16.9340 16.8668 17.3575 17.1244 16.9196 16.7061 16.5157 16.3227 16.1489 15.9765 15.8208 15.6689 15.5316 15.3999 15.2812 15.1689 15.7618 15.5145 15.2577 15.0297 14.7990 14.5908 14.3840 14.1955 14.0110 13.8419 13.6783 13.5281 13.3843 13.2522 13.6286 13.3463 13.1002 12.8516 12.6296 12.4093 12.2093 12.0133 11.8336 11.6593 11.4984 11.3436 11.2004 11.0636 10.8816 10.6431 10.4024 10.1909 9.9813 9.7930 9.6086 9.4404 9.2772 9.1269 8.9820 8.8477 8.7191 8.5995 7.6161 7.4167 7.2449 7.0745 6.9236 6.7758 6.6423 6.5127 6.3940 6.2796 6.1738 6.0722 5.9778 5.8877 3.9171 3.8168 3.7170 3.6300 3.5447 3.4684 3.3944 3.3270 3.2620 3.2022 3.1448 3.0915 3.0405 2.9930
figure(1)
mesh(x,t,T.')
xlabel('Distance(m)')
ylabel('Temperature(\circC)')
zlabel('T, whatever that is')

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