-- FreeFem++ v4.6 (Thu Apr  2 15:47:38 CEST 2020 - git v4.6)
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  channel_stokes_steady.edp
    2 : //
    3 : //  Discussion:
    4 : //
    5 : //    Solve the steady Stokes equations.
    6 : //
    7 : //  Location:
    8 : //
    9 : //    http://people.sc.fsu.edu/~jburkardt/freefem_src/channel_stokes_steady/channel_stokes_steady.edp
   10 : //
   11 : //  Modified:
   12 : //
   13 : //    18 May 2015
   14 : //
   15 : //  Author:
   16 : //
   17 : //    Florian De Vuyst
   18 : //
   19 : //  Reference:
   20 : //
   21 : //    Florian De Vuyst,
   22 : //    Numerical modeling of transport problems using freefem++ software -
   23 : //    with examples in biology, CFD, traffic flow and energy transfer,
   24 : //    HAL id: cel-00842234
   25 : //    https://cel.archives-ouvertes.fr/cel-00842234
   26 : //
   27 : cout << "\n";
   28 : cout << "channel_stokes_steady:\n";
   29 : cout << "  FreeFem++ version.\n";
   30 : cout << "  Solve Stokes equations for steady flow in a cha
  ... : nnel.\n";
   31 : 
   32 : real Re = 600.0;
   33 : real nu = 1.0 / Re;
   34 : real Lx = 12.0;
   35 : real Ly = 5.0;
   36 : real dt = 0.5;
   37 : //
   38 : //  Set the boundary.
   39 : //
   40 : border c1 ( t=0,1 )    { x=t*Lx; y=0; }
   41 : border c2 ( t=0,1 )    { x=Lx; y=t*Ly; }
   42 : border c3 ( t=1,0 )    { x=t*Lx; y=Ly; }
   43 : border c4 ( t=1,0 )    { x=0; y=t*Ly; }
   44 : border c5 ( t=2*pi,0 ) { x=4+0.2*cos(t); y=Ly/2+0.2*sin(t); }
   45 : border c6 ( t=0,1 )    { x=5+Lx/2*t; y=Ly/2+0.4; }
   46 : border c7 ( t=0,1 )    { x=5+Lx/2*t; y=Ly/2-0.4; }
   47 : //
   48 : //  Make the mesh.
   49 : //
   50 : mesh Th = buildmesh 
   51 : (
   52 :   c1(80)+c2(40)+c3(80)+c4(20)+c5(60)+c6(100)+c7(100)
   53 : );
   54 : 
   55 : plot ( Th, wait = 1, ps = "channel_stokes_steady_mesh.ps" );
   56 : //
   57 : //  Define discrete velocity space Uh and discrete pressure space Vh.
   58 : //
   59 : fespace Uh ( Th, P2 );
   60 : fespace Vh ( Th, P1 );
   61 : Uh u;
   62 : Uh v;
   63 : Uh uh;
   64 : Uh vh;
   65 : Uh uold;
   66 : Uh vold;
   67 : Vh p;
   68 : Vh ph;
   69 : Vh uplot;
   70 : Vh vplot;
   71 : Vh vort;
   72 : //
   73 : //  Define the weak form of the steady state Stokes equations.
   74 : //
   75 : real eps = 1.0E-10;
   76 : 
   77 : problem stokes ( [u,v,p], [uh,vh,ph] ) =
   78 :     int2d(Th) ( nu*dx(u)*dx(uh) + nu*dy(u)*dy(uh) )
   79 :   + int2d(Th) (nu*dx(v)*dx(vh) + nu*dy(v)*dy(vh) )
   80 :   - int2d(Th) (p*dx(uh))
   81 :   - int2d(Th) (p*dy(vh))
   82 :   - int1d(Th, c2) (nu*dx(u)*N.x*uh+nu*dy(u)*N.y*uh)
   83 :   - int1d(Th, c2) (nu*dx(v)*N.x*vh+nu*dy(v)*N.y*vh)
   84 :   + int2d(Th) (dx(u)*ph + dy(v)*ph)
   85 :   + int2d(Th) (eps*p*ph)
   86 :   + on ( c1, c3, c5, u=0, v=0)
   87 :   + on ( c4, u=4.0 * y/Ly * (1-y/Ly), v=0 );
   88 : //
   89 : //  Solve the equations.
   90 : //
   91 : stokes;
   92 : //
   93 : //  Plot the velocity vector field.
   94 : //
   95 : uplot = u;
   96 : vplot = v;
   97 : plot ( Th, [uplot,vplot], wait = 1, fill = 1, 
   98 :   ps = "channel_stokes_steady_velocity.ps", cmm = "channel_stokes_steady velocity" );
   99 : //
  100 : //  Plot the pressure field.
  101 : //
  102 : plot ( Th, p, wait = 1, fill = 1, ps = "channel_stokes_steady_pressure.ps", 
  103 :   cmm = "channel_stokes_steady pressure" );
  104 : //
  105 : //  Terminate.
  106 : //
  107 : cout << "\n";
  108 : cout << "channel_stokes_steady:\n";
  109 : cout << "  Normal end of execution.\n";
  110 : 
  111 :  sizestack + 1024 =3768  ( 2744 )


channel_stokes_steady:
  FreeFem++ version.
  Solve Stokes equations for steady flow in a channel.
  --  mesh:  Nb of Triangles =  16814, Nb of Vertices 8547
  -- Solve : 
          min -3.46506e-34  max 1.02772
          min -0.251782  max 0.251782
          min -0.00431818  max 0.0166723

channel_stokes_steady:
  Normal end of execution.
times: compile 0.005592s, execution 11.6418s,  mpirank:0
 CodeAlloc : nb ptr  3952,  size :496656 mpirank: 0
Ok: Normal End