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// -*- c++ -*-

//  This file is part of ff3d - http://www.freefem.org/ff3d
//  Copyright (C) 2003  Laboratoire J.-L. Lions UPMC Paris

//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2, or (at your option)
//  any later version.

//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.

//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software Foundation,
//  Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  

//  $Id: stokes.ff,v 1.5 2005/11/28 00:54:32 delpinux Exp $

// Stokes equations

vector n = (20,20,20);
vertex A = (0,0,0);
vertex B = (1,1,1);

scene S = pov("stokes.pov");
mesh M = structured(n,A,B);
domain Omega = domain(S,outside(<1,0,0>));

function teta0 = 0;
double eps = 1e-5;

solve(u1,u2,u3,p) in Omega by M
    krylov(precond=diagonal,type=bicg),
    cg(epsilon=1e-5) {

	test(U1,U2,U3,P)
	  int(grad(u1)*grad(U1) - p*dx(U1)
	      +grad(u2)*grad(U2) - p*dy(U2)
	      +grad(u3)*grad(U3) - p*dz(U3)
	      -eps*grad(p)*grad(P) - eps*p*P
	      -dx(u1)*P - dy(u2)*P - dz(u3)*P) = 0;

	u1 = 0 on M xmin;
	u1 = 0 on M xmax;
	u1 = 0 on M ymin;
	u1 = 1 on M ymax;
	u1 = 0 on M zmin;
	u1 = 0 on M zmax;
	u1 = 0 on <1,0,0>;

	u2 = 0 on M;
	u2 = 0 on <1,0,0>;

	u3 = 0 on M;
	u3 = 0 on <1,0,0>;
    };

// Post-processing
mesh T = tetrahedrize(Omega,M);
save(medit,"stokes-u",T);
save(medit,"stokes-u",[u1, u2, u3],T);
save(medit,"stokes-p",T);
save(medit,"stokes-p",p,T);