[LearnerJosh]

Develop a numerical code to solve steady state 1d heat conduction equation with source term using the TDMA algorithm
(a) Solve a 1d conduction problem with a point heat source at the centre and constant temperature boundary conditions.
(b) Compare the results with the analytical solution for the same case on the same plot (Temperature vs x )

[aerosayan]

Is this a homework question?


It's easy to solve, however if it is a homework question, the instructor should have provided you with proper tutorials on solving the heat conduction using explicit formulation first, then he/she should have taught you how to code the TDMA algorithm, then he/she should've taught you how to form the implicit form of the heat conduction equation and then solve the resultant matrix using your previously developed TDMA algorithm.


For the implicit formulation of the 1D heat conduction equation, you can refer Vertsteeg's book (I think somewhere between chapter 5 to 7. I can't recall correctly). In those chapters, the discretization procedure is shown and proper results are given so that you can verify your own calculations.

[LearnerJosh]

Originally Posted by aerosayan

Is this a homework question?


It's easy to solve, however if it is a homework question, the instructor should have provided you with proper tutorials on solving the heat conduction using explicit formulation first, then he/she should have taught you how to code the TDMA algorithm, then he/she should've taught you how to form the implicit form of the heat conduction equation and then solve the resultant matrix using your previously developed TDMA algorithm.


For the implicit formulation of the 1D heat conduction equation, you can refer Vertsteeg's book (I think somewhere between chapter 5 to 7. I can't recall correctly). In those chapters, the discretization procedure is shown and proper results are given so that you can verify your own calculations.

Yes, it is a homework question. Thank you for your help.

[LuckyTran]

TDMA pseudo code is on wikipedia.

You can just google TDMA + whatever software you are using and quickly find a working TDMA. Then it's just applying the constraints given, i.e. setting up the right matrix. But actually, only certain discretizations results in a tridiagonal matrix which can then efficiently be solved using the TDMA. And although we can more-or-less guess what discretization is being applied, that really should be part of the problem definition.