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How to find a good initial guess for a BVP

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Old   January 25, 2010, 17:32
Smile How to find a good initial guess for a BVP
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Yan Yan
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Hi All,
Can anyone please share some hints on how to find a good inital guess?

I am solving a nonlinear BVP(steady-states) extracted from a time-dependent problem by setting d/dt=0. The equation is conservational law for mass, momentum, internal energy, with an algebraic heating source. v(velocity), P(pressure), U(fluid internal energy), can be solved from this coupled system.

I am using Newton's method for this nonlinear system. Frankly, I do not have a good initial guess for the solver. The only information that I have is the inital condition for the time-dependent problem, where the BVP comes from. I have runned my solver with different inital guess many times, but with no luck of a satisfying residual reduction.

So, do I have to solve the time-dependent problem after a long time stepping to get a steady solution? Or is there any better way of finding a good initial guess?

Any suggestion is highly appreciated.

Yan
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Old   January 25, 2010, 22:51
Default Implicit time-stepping to Newton
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I think I've read this issue in a CFD book (Fletcher's book?).

You may want to add a time term to the Jacobian (just like an implicit time-stepping), and guadually take the time step to infinity (so that the time term goes to zero and finally the method reduces to the Newton iteration). Small time step enlarges the radius of convergence.

Good luck.
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Old   January 26, 2010, 12:31
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Yan Yan
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Thanks for the reply.

I think I will try continuation method as suggested by an expert. I have not read anything about that. But I will start soon

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Old   January 27, 2010, 14:05
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Yan Yan
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Hi Gory,
Just to confirm that I did find a chapter on steady-state problem in Fletcher's book. Also what you said is exactly continuation method.

Again, thanks a lot for providing the reference.

Yan
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