19 August 2018 03:16:02 PM

FEM2D_NAVIER_STOKES
  C++ version:

  Compiled on Aug 19 2018 at 14:18:58.

  Finite element solution of the 
  steady incompressible Navier Stokes equations
  on a triangulated region in 2 dimensions.'

  - nu * ( Uxx + Uyy ) + UUx + VUy + dPdx = F1(x,y)
  - nu * ( Vxx + Vyy ) + UVx + VVy + dPdy = F2(x,y)
                                  Ux + Vy = F3(x,y).

  Boundary conditions may be of Dirichlet type:

    U(x,y) = U_BC(x,y)
    V(x,y) = V_BC(x,y)
    P(x,y) = P_BC(x,y)

  or of Neumann type with zero right hand side:

    dU/dn(x,y) = 0
    dV/dn(x,y) = 0
    dP/dn(x,y) = 0

  The finite element method uses Taylor-Hood
  triangular elements which are linear for pressure
  and quadratic for velocity.

  Maximum number of Newton iterations IT_MAX = 5
  Quadrature order =           7
  The kinematic viscosity NU = 1

  Current status:

  * testing zero Neumann condition option.

  Node file is "nodes6.txt".
  Element file is "triangles6.txt".
  Number of nodes =          65

  First 10 nodes

  Row:       1             2       
  Col

    1              0             0
    2              0          0.25
    3              0           0.5
    4              0          0.75
    5              0             1
    6           0.25             0
    7           0.25          0.25
    8           0.25           0.5
    9           0.25          0.75
   10           0.25             1


  Element order =            6
  Number of elements =       24

  First 10 elements

  Row:        1         2         3         4         5         6  
  Col

    1         1        11         3         6         7         2  
    2        13         3        11         8         7        12  
    3         3        13         5         8         9         4  
    4        15         5        13        10         9        14  
    5        11        21        13        16        17        12  
    6        23        13        21        18        17        22  
    7        13        23        15        18        19        14  
    8        25        15        23        20        19        24  
    9        21        31        23        26        27        22  
   10        33        23        31        28        27        32  


  Dirichlet boundary condition on pressure
  will be applied at node 1

  Number of Neumann conditions added = 6

  Boundary conditions per node:

      Node    U_cond    V_cond    P_cond

         0         2         2         2
         1         2         2         0
         2         2         2         1
         3         2         2         0
         4         2         2         1
         5         2         2         0
         6         1         1         0
         7         1         1         0
         8         1         1         0
         9         2         2         0
        10         2         2         1
        11         1         1         0
        12         1         1         1
        13         1         1         0
        14         2         2         1
        15         2         2         0
        16         1         1         0
        17         1         1         0
        18         1         1         0
        19         2         2         0
        20         2         2         1
        21         1         1         0
        22         1         1         1
        23         1         1         0
        24         2         2         1
        25         2         2         0
        26         1         1         0
        27         1         1         0
        28         1         1         0
        29         2         2         0
        30         2         2         1
        31         1         1         0
        32         1         1         1
        33         1         1         0
        34         2         2         1
        35         2         2         0
        36         1         1         0
        37         1         1         0
        38         1         1         0
        39         2         2         0
        40         2         2         1
        41         1         1         0
        42         1         1         1
        43         1         1         0
        44         2         2         1
        45         2         2         0
        46         1         1         0
        47         1         1         0
        48         1         1         0
        49         2         2         0
        50         2         2         1
        51         1         1         0
        52         1         1         1
        53         1         1         0
        54         2         2         1
        55         2         2         0
        56         1         1         0
        57         1         1         0
        58         1         1         0
        59         2         2         0
        60         2         2         1
        61         3         3         0
        62         3         3         1
        63         3         3         0
        64         2         2         1

  Total number of variables is 151

  Variable indices per node:

      Node   U_index   V_index   P_index

         1         1         2         3
         2         4         5        -1
         3         6         7         8
         4         9        10        -1
         5        11        12        13
         6        14        15        -1
         7        16        17        -1
         8        18        19        -1
         9        20        21        -1
        10        22        23        -1
        11        24        25        26
        12        27        28        -1
        13        29        30        31
        14        32        33        -1
        15        34        35        36
        16        37        38        -1
        17        39        40        -1
        18        41        42        -1
        19        43        44        -1
        20        45        46        -1
        21        47        48        49
        22        50        51        -1
        23        52        53        54
        24        55        56        -1
        25        57        58        59
        26        60        61        -1
        27        62        63        -1
        28        64        65        -1
        29        66        67        -1
        30        68        69        -1
        31        70        71        72
        32        73        74        -1
        33        75        76        77
        34        78        79        -1
        35        80        81        82
        36        83        84        -1
        37        85        86        -1
        38        87        88        -1
        39        89        90        -1
        40        91        92        -1
        41        93        94        95
        42        96        97        -1
        43        98        99       100
        44       101       102        -1
        45       103       104       105
        46       106       107        -1
        47       108       109        -1
        48       110       111        -1
        49       112       113        -1
        50       114       115        -1
        51       116       117       118
        52       119       120        -1
        53       121       122       123
        54       124       125        -1
        55       126       127       128
        56       129       130        -1
        57       131       132        -1
        58       133       134        -1
        59       135       136        -1
        60       137       138        -1
        61       139       140       141
        62       142       143        -1
        63       144       145       146
        64       147       148        -1
        65       149       150       151

  The matrix half bandwidth is 25
  The matrix bandwidth is      51
  The storage bandwidth is     76

  Order 6 nodes plotted in "nodes6.eps".

  Order 6 triangles plotted in "triangles6.eps".

  Pressure nodes written to "nodes3.txt".

  Pressure triangles written to "triangles3.txt".

  l2-norm of FEM residual = 1.28019

  l2-norm of adjusted FEM residual = 2.61618e-14

  Convergence.

  Solution to the NAVIER STOKES Equations:

      Node               U               V               P

         0               0               0              10
         1          0.1875     8.32667e-17
         2            0.25              -0              10
         3          0.1875      -2.498e-16
         4               0               0              10
         5               0               0
         6          0.1875     5.74193e-13
         7            0.25     1.40628e-14
         8          0.1875    -4.05925e-15
         9               0               0
        10               0              -0               9
        11          0.1875    -3.07431e-14
        12            0.25     2.87237e-14               9
        13          0.1875     7.47903e-14
        14               0               0               9
        15       4.996e-16               0
        16          0.1875    -8.29512e-14
        17            0.25     2.70516e-14
        18          0.1875     4.23138e-14
        19               0               0
        20               0               0               8
        21          0.1875    -1.69508e-14
        22            0.25     -6.6602e-15               8
        23          0.1875    -1.25081e-14
        24               0               0               8
        25              -0               0
        26          0.1875     1.06638e-15
        27            0.25    -1.04145e-14
        28          0.1875    -1.34215e-14
        29               0               0
        30               0               0               7
        31          0.1875     7.97169e-15
        32            0.25     2.28377e-16               7
        33          0.1875    -2.59113e-17
        34               0               0               7
        35              -0               0
        36          0.1875     4.11128e-15
        37            0.25     2.01857e-15
        38          0.1875     2.49373e-15
        39               0               0
        40               0               0               6
        41          0.1875    -1.72547e-15
        42            0.25     6.34575e-16               6
        43          0.1875     1.50216e-15
        44               0               0               6
        45              -0               0
        46          0.1875    -1.78911e-15
        47            0.25     5.66503e-17
        48          0.1875     4.45544e-16
        49               0               0
        50               0               0               5
        51          0.1875    -4.77301e-16
        52            0.25    -4.06083e-16               5
        53          0.1875    -4.53386e-16
        54               0               0               5
        55     1.66533e-16               0
        56          0.1875     1.38481e-16
        57            0.25    -5.26027e-17
        58          0.1875    -2.28813e-16
        59               0               0
        60               0               0               4
        61          0.1875     4.04259e-16
        62            0.25     1.70221e-16               4
        63          0.1875      6.5553e-17
        64               0               0               4

  Navier Stokes pressures written to "pressure3.txt".

  Navier Stokes velocities written to "velocity6.txt".

FEM2D_NAVIER_STOKES:
  Normal end of execution.

19 August 2018 03:16:02 PM