Finite Difference Time Steps?

[ModManSEK]

I am using a finite-difference thermal solver to evaluate a transient heat-transfer problem. I have chosen an implicit forward/backward (i.e., central) differencing method. The problem is with the time step. If I choose a time step twice as large as the software calculates, I seem to get reasonable answers. If I choose a time step half as large, I get an unstable solution or at least one that seems to be nonsensical. This seems to fly in the face of theory. I always thought using a smaller time step resulted in a longer solution time, not an unstable solution. Does anyone have any experience with this? (My problem involves radiation to space and orbital heating.) Thanks in advance.

 

[JJPage]

Your right to expect a more stable system when using smaller time steps. I don't quite understand your observation. It is possible that the "1/2" time step used hits on a (calculation)harmonic in the equation set. If so, the instability should not appear when the calculations are done with a time step about 15% faster and slower. (It may also tell you something about the natural harmonics of the physical situation.) If the calculation harmonic still appears, then I am stumped. If the instability continues to be "become worse, as the time step gets smaller", but changes personality, then the system is acting very odd indeed. More awareness of the equation set would be needed to understand it. Find a GOOD math guy.

 

[ModManSEK]

Thanks for your input JJPage. I subsequently discovered (with a little help from the software vendor) that the problem was due to round-off error. At each calculation step in a finite-differences analysis, there is always some round off. Round-off increases as the number of calculations increases (i.e., as time-step is decreased).

Conversely, due to the mathematical nature of finite-difference approximations, truncation or discretization errors can result if the time step is too large. So the trick is in minimizing the errors from both by choosing an appropriate time step. Unless you have a priori knowledge of what the solution should be, this "trick" becomes even trickier. I eventually was able to compare my results with another analysis and was then able to correct the mistake. Thanks again for your input.