Solving PDEs using fsolve

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patilak
patilak 2016-7-18
回答： Torsten 2016-7-19
I am trying to solve continuity, Navier-Stokes and heat transfer equation in 2-D cylindrical coordinates. I have discretized these equations. So now I have 4 non linear equations with 4 variables(u,v,T,f) such that: f1(u,v)=0 f2(u,v,f)=0 f3(u,v,f)=0 f4(u,v,f,T)=0
u-Axial velocity v-Radial velocity T-temperature f-liquid fraction (my problem involves solidification of metal)
Can I solve these using fsolve?

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回答（3 个）

Alan Weiss
Alan Weiss 2016-7-18
I do not understand how you propose to parameterize your problem so that fsolve would be appropriate. Don't you need to put a PDE solver in the solution process somehow?
Alan Weiss
MATLAB mathematical toolbox documentation
patilak
patilak 2016-7-18
For two-dimensional PDE, PDE solver would only be the PDE toolbox?
Torsten
Torsten 2016-7-19
If your problem is stationary and you discretized your equations and boundary conditions correctly, this results in a big nonlinear system of equations for the solution variables in each grid point. So yes: fsolve can be used for solution if the size of your system is moderate.
Best wishes
Torsten.

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