Solving PDEs using fsolve

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?

Answer 1

[Alan Weiss]

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

Answer 2

[patilak]

For two-dimensional PDE, PDE solver would only be the PDE toolbox?

Answer 3

[Torsten]

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.