On 11/01/09 11:29 AM, Hatef Monajemi wrote:
> Refer to attached file please!
Why are you sending plain text file in binary form? This way you are
limiting your audience.
I can't aswer your questions, but I can convert it into more readable
format:
=======
Hello
I am trying to figure out how to model a Nonlinear problem in dolfin in
which there is more than one variable, say(u,p). There is currently some
documents in "demo" and "bench/fem/assembly" which deals with nonlinear
problmes, but in both of them there exist just one variable. I was
wondering how the coding process changes when there is coupled PDEs (for
instance solving Navier-Stokes equation). Based on what I found on
threads, I could think of augmenting the solution function by defining
subfunctions, However I think something must have been missed since I do
not get convergence. I have modeled the same coupled problem assuming
linearity witout having any problem, but when a nonlinear term comes in,
it is a bit vague for me how to handle it in dolfin setting. The
procedure I am following is as follows: (based on nonlinear-poisson demo
and other docs)
----------------------------------------------------------
1)Defining fuction for source and BCs
2)Define subdomain for BCs
3)Read Mesh and Subdomain marker
4)pseudo time
real t = 0.0;
5)Source term and initial conditions
Function Un(mesh,2, 0.0);
Function Pn(mesh,0.0);
Function f(mesh,2,0.0);
XvelNoslip xvelnoslip(mesh);
YvelNoslip yvelnoslip(mesh);
VelNoslip velnoslip(mesh);
Inflow inflow(mesh,&t);
6)Define SubSystems
SubSystem velocity(0);
SubSystem pressure(1);
7)solution vectors
Function U0;
Function P0;
8)set up Form
NonlinearproblemBilinearForm a(U0) ;
NonlinearproblemLinearForm L_1(Un,U0,Pn,P0,f);
9)Solve system
Vector x;
Function u(mesh,x,a);
10)Extract sub functions
U0 = u[0];
P0 = u[1];
11)set up boundary condition
DirichletBC bc0(xvelnoslip,sub_domains,0 , velocity);
DirichletBC bc1(yvelnoslip,sub_domains,1, velocity);
DirichletBC bc2(velnoslip,sub_domains,2, velocity);
DirichletBC bc3(inflow,sub_domains,2, pressure);
12)collect all the BCs
Array<BoundaryCondition*> bcs(&bc0,&bc1,&bc2,&bc3);
13)parameters for time stepping
real T = 0.005;
real k = 0.001;
14)time stepping
Progress p("Time-stepping");
while ( t < T )
{
NonlinearPDE pde(a,L_1,mesh,bcs);
15) Solve nonlinear problem in a series of steps
real ds = 1.0; real S = 3.0;
pde.solve(u,t,S,ds);
16) Save the Solutions
17) Move to next interval
p = t / T;
t += k;
Un= U0;
Pn= P0;
}
-----------------------------------------------------------------------------
I would appreciate if anyone could give me any suggustions on how to
consider a "Coupled Nonlinear PDE system" in Dolfin or at least guide me
to the right place where I can find some documents on that.
Thanks,
Hatef
>
> --------------------------------------
> Hatef Monajemi Graduate Student Dept of Civil and Environmental Eng 2032 MC
> Building, Carleton University 1125 Colonel By Drive, Ottawa Ontario, Canada,
> K1S
> 5B6
>
>
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