larger time step brings convergence instead of smaller time step
 

I am having my model to convergence with larger time step as 10s instead of 1s. I do not understand why is it so since in common sense smaller time step is much accurate and much accurate. Please help. Why is it so?

Dear Raymond,

It's not strange! As you know, convergency and accuracy are two different things. In linear cases, a consistent and stable case is certainly convergent but in non linear cases they are necessary conditions but not sufficient for convergency. But accuracy in both cases is totally different; by reducing your time step, accuracy is improved but we don't have a general rule for convergency in non linear cases.
I think that if your numerical procedure is correct, we can conclude that when you set dt= 10 sec your case is convergent to wrong results but in dt= 1 sec, there would be a potential to reach to accurate results but it faces convergency issues which can be resolved by lowering time step or other techniques. hope that help you.

Bests,

Thanks Amir. My model shows me error and unable to run if I am using time step size=1s. I accidentally using larger time step size=10s and the model is able to run but it is unable to be validated with my experiment results due to its different pattern in results. I am using even larger time step size=20s and the results are much reasonable compared to time step size=10s. I am using the default setting of coupled algorithm with courant number=200. Is it too big? Is it the main factors affecting my results? I do not understand why larger time step size much better from smaller time step size from views of accuracy and convergence? I afraid that that is due to wrong setting to the model since I need that model to simulate another studies. Please help. Thanks for your help.

Dear Raymond,

Certainly, reducing time step can improve temporal accuracy but in coupled form of solvers, courant No has its own effects. Although for your case the default setting is 200 which means that in linear form it's unconditionally stable but non linear form has some restriction over that, so it's recommended to start with lower courant No and then increase it in some stages. I suggest you to read chapter 25 of user guide which can really help you.

Bests,

hi,
in addition to what amir said, you can try checking and changing some boundary conditions and settings if needed and dont forget about the grid. bad grid can do anything you never thought! but after all, explainig more about your case and the options you've chosen can bring you more useful helps.
yours,
mohammad

Hi,
I am new to the forum and i was searching an answer for a similar problem. I have been asked to perform Gauss-Seidel methods(point,line and line succesive over-relaxation) on a linear 2-D elliptic PDE. So i wrote a Fortran code for it. The problem starts from here. After i got the result from my code, i compared them with reference textbook results. The control sequence in the code(relative error) seems fine but absolute error was huge(sometimes 20%). Then i realised, the reference textbook step size was 0.05 where my instructions dictates 0.02. I rerun them with reference textbook stepsize and the results are perfect match. Now you see i am confused and i am searching an explanation to write in my report. Here is what i tried so far.

- I derived modified equation of the elliptic equation and artificial viscosity is the governing error. However, isnt 20% absolute error is quite high for artificial viscosity?
- I theorized the reference textbook results was not converged solution so it was amistake by the authors(chances are slim since the authors are expert)
- My original method discretzed it as Centrel Space Differencing Scheme, i tried backward the results does converge but error is quite high(since they are first order)
- Last theory is about round-off errors. I thought maybe change in 0.02 step size is too low to be recognized by the code. So i tried doubles in fortran. Same thing happens.

So do you think any other possible reason for getting lowr accuracy with lower step sizes?

best regards,
mtaskin