FTCS Error Residuals

anonymousbach · April 4, 2015, 15:34

Hi All,

I am trying to solve a 2D transient heat problem using a FTCS Finite Difference, Explicit Scheme. The system is rectangular domain, with constant 0 deg C on the longer (side) walls and two different, positive temperatures at the top and bottom (also constant). Now, my code converges to the desired criteria, the values seem reasonable.

Overall, my average %error compared to an exact solution is around 7.2%, but in one corner the error peaks at about 70% and along one wall, it averages around 50%. Hopefully you can see the image I've attached to give a clearer picture.

What makes me worries is these errors seem unaffected by timestep. Are errors like this common in using FTCS schemes with a fairly coarse grid? Can anyone think of any reason why I'm having these unusual errors?

As always, any help would be greatly appreciated.

FMDenaro · April 4, 2015, 17:17

1) what about the exact solution you used?
2) in the errors plot, are you visualizing only the inner nodes?
3) the errors are computed at the steady state?

April 4, 2015, 15:34	FTCS Error Residuals	#1
anonymousbach New Member anonymous Join Date: Apr 2015 Posts: 7 Rep Power: 11	Hi All, I am trying to solve a 2D transient heat problem using a FTCS Finite Difference, Explicit Scheme. The system is rectangular domain, with constant 0 deg C on the longer (side) walls and two different, positive temperatures at the top and bottom (also constant). Now, my code converges to the desired criteria, the values seem reasonable. Overall, my average %error compared to an exact solution is around 7.2%, but in one corner the error peaks at about 70% and along one wall, it averages around 50%. Hopefully you can see the image I've attached to give a clearer picture. What makes me worries is these errors seem unaffected by timestep. Are errors like this common in using FTCS schemes with a fairly coarse grid? Can anyone think of any reason why I'm having these unusual errors? As always, any help would be greatly appreciated.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Using FTCS to solve a reduced form of Navier-Stokes eqn	DA6righthand	Main CFD Forum	8	April 2, 2015 04:14

April 4, 2015, 17:17		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	1) what about the exact solution you used? 2) in the errors plot, are you visualizing only the inner nodes? 3) the errors are computed at the steady state?