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Topic: Linear system of Hydrodynamic solving by means of PDE toolbox
Replies: 13   Last Post: Jan 16, 2014 10:05 PM

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Torsten

Posts: 1,459
Registered: 11/8/10
Re: Linear system of Hydrodynamic solving by means of PDE toolbox
Posted: Jan 8, 2014 9:07 AM
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"Bill Greene" wrote in message <lajkp6$mce$1@newscl01ah.mathworks.com>...
> The answer to your second question is to call the pdegrad function with
> the solution vector.
> http://www.mathworks.com/help/pde/ug/pdegrad.html
>
> Regarding your first question, where are you stuck? If you post the code you
> have so far and describe the point of your confusion, we might be able to help.
>
> Bill
>
> "Sergey" wrote in message <lain4d$9uh$1@newscl01ah.mathworks.com>...

> > Alright, If there is no idea how the problem can be solved directly (I've stuck as well) Maybe someone could tell me how to get the Phi_z (= dPhi / dz) from the solution of the Laplace equation of PDE toolbox? It gives result on the unstructured grid, that I can't directly differentiate by the usual scheme like (Phi(2,1) - Phi(1,1))/dz.
> >
> > "Sergey" wrote in message <la2vkf$rrb$1@newscl01ah.mathworks.com>...

> > > Dear Matlab users and developers,
> > >
> > > I need to solve the following PDE system in 2D space:
> > > (1) div(grad( Phi )) = 0 |any x, any z;
> > > (2) Eta_t = Phi_z | any x, z = 0;
> > > (3) Phi_t = -g*Eta | any x, z = 0.
> > > where "?_t" - time derivative, "?_z" - z - axis derivative, "div" - divergence operator, "grad" - gradient operator.
> > > (1) - simple Laplace equation for interior flow potential,
> > > (2) - surface elevation (Eta) and the potential (Phi) connection,
> > > (3) - linearized Bernoulli equation.
> > > It is the linearized equations of hydrodynamics. Of course I could solve it using just a FD scheme, but if there is a possibility to utilize some internal Matlab tools like PDE toolsbox, it is preferable to use, since it is already developed and verified.
> > > I know, that the PDE toolbox provide a possibility to solve the 2D Laplace equation. What about the rest of the system? Can I somehow couple all the equations by means of the PDE toolbox functionality?
> > >
> > > Sincerely,
> > > -Sergey


The OP needs the gradient at the boundary surface z=0.
This is also possible with pdegrad ? What about the accuracy ?

Best wishes
Torsten.



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