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September 21, 2015, 19:18 |
stability comparison
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#1 |
Senior Member
Join Date: Jun 2010
Posts: 111
Rep Power: 16 |
I have used two method to solve a system of nonlinear equation, with the same number of time steps, mesh, and solver, etc. Can I comment on the stability of the two methods, based on the largest time step sizes that still produces stable results? (I know it will not be a definite proper stability analysis) - any other suggestions are also welcome.
Also, if I the results seem stable, but the CFL is no longer satisfied with the larger time steps, it is correct to take the step size at which CFL condition is not satisfied as the largest step size, even though the results may seem stable? |
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September 22, 2015, 02:20 |
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#2 | ||
Senior Member
Lucky
Join Date: Apr 2011
Location: Orlando, FL USA
Posts: 5,762
Rep Power: 66 |
Quote:
Quote:
Flux inhibitors and gradient limiters also help improve stability, by a lot, and this generally isn't accounted for. Both physical & numerical diffusion also improve stability. |
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September 22, 2015, 04:41 |
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#3 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73 |
generally, for a convection-diffusion 3d problem, the numerical stability implies the existence of a region of stability...that is a hypersurface being cx,cy,cz, alphax,alphay,alphaz the numerical parameters..
and the Neumann analysis gives a response only for the linear case.. |
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September 22, 2015, 05:02 |
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#4 |
Senior Member
Join Date: Jun 2010
Posts: 111
Rep Power: 16 |
Thank you LuckyTran. Would another (crude) approach be to compare the time the calculations take to reach convergence?
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Tags |
converg condition, eigenvalues, nonlinear systems, numerical error, stability analysis |
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