dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Mon, Jan 12, 2009 at 11:06:27AM -0700, Bartosz Sawicki wrote:
> 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

Please try the latest DOLFIN version (0.9.0) and then ask again.

-- 
Anders

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