Transient heat conduction problem
- December 4, 2019
- 1 reply
- 1355 views
Hi all,
I am working on a problem for my class and I'm having trouble even beginning to program this transient heat conduction problem.
I have attached a sheet with information regarding the problem I am trying to solve. What I want to do is eventually increase the order of my interpolation functions (from linear to quadratic and so on) and also increase the number of elements I use and compare how well each of these methods converge, but I don't know how to incorporate iterating through time into my dependent variable while still keeping it a 2x1 vector.
Basically, I have a boundary condition at u1 for all timesteps and and an initial condition at t=0 for all x, but short of adding another index onto my u vector, I don't know how to actually iterate through a number-of-timesteps value. I don't think I can add another index onto the u vector because then that would change the outcome when I multiply my matrices by that vector.
The difference scheme I want to use (in terms of variable names in my sheet) is:
[K.hat] * {u}(s+1) = [K.bar] * {u}(s) + 1/4*{Q}(s+1) + 1/4{Q}(s)
Where s is the time step value.