Torsten
Posts:
1,472
Registered:
11/8/10


Re: Linear system of Hydrodynamic solving by means of PDE toolbox
Posted:
Jan 8, 2014 9:07 AM


"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.

