28 December 2010 10:01:42.510 AM FREE_FEM_NAVIER_STOKES FORTRAN90 version: Finite element solution of the the steady incompressible Navier Stokes equations on a triangulated grid 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 = 1.00000 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 0.00000 0.00000 2 0.00000 0.250000 3 0.00000 0.500000 4 0.00000 0.750000 5 0.00000 1.00000 6 0.250000 0.00000 7 0.250000 0.250000 8 0.250000 0.500000 9 0.250000 0.750000 10 0.250000 1.00000 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 1 2 2 2 2 2 2 0 3 2 2 1 4 2 2 0 5 2 2 1 6 2 2 0 7 1 1 0 8 1 1 0 9 1 1 0 10 2 2 0 11 2 2 1 12 1 1 0 13 1 1 1 14 1 1 0 15 2 2 1 16 2 2 0 17 1 1 0 18 1 1 0 19 1 1 0 20 2 2 0 21 2 2 1 22 1 1 0 23 1 1 1 24 1 1 0 25 2 2 1 26 2 2 0 27 1 1 0 28 1 1 0 29 1 1 0 30 2 2 0 31 2 2 1 32 1 1 0 33 1 1 1 34 1 1 0 35 2 2 1 36 2 2 0 37 1 1 0 38 1 1 0 39 1 1 0 40 2 2 0 41 2 2 1 42 1 1 0 43 1 1 1 44 1 1 0 45 2 2 1 46 2 2 0 47 1 1 0 48 1 1 0 49 1 1 0 50 2 2 0 51 2 2 1 52 1 1 0 53 1 1 1 54 1 1 0 55 2 2 1 56 2 2 0 57 1 1 0 58 1 1 0 59 1 1 0 60 2 2 0 61 2 2 1 62 3 3 0 63 3 3 1 64 3 3 0 65 2 2 1 Total number of variables is 151 Variable indices per node: Node U V P 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 = 0.273050E-13 Convergence. Solution to the NAVIER STOKES Equations: Node U V P 1 0.00000 0.00000 0.00000 2 0.187500 0.108912E-15 3 0.250000 -0.533262E-16 -0.435780E-10 4 0.187500 0.208167E-15 5 0.00000 0.00000 -0.399737E-10 6 0.00000 0.00000 7 0.187500 0.593608E-12 8 0.250000 0.157504E-13 9 0.187500 -0.277494E-14 10 0.00000 0.00000 11 0.00000 0.624500E-16 -1.00000 12 0.187500 -0.319900E-13 13 0.250000 0.305626E-13 -1.00000 14 0.187500 0.780410E-13 15 0.00000 0.00000 -1.00000 16 0.333067E-15 0.00000 17 0.187500 -0.860121E-13 18 0.250000 0.280432E-13 19 0.187500 0.439499E-13 20 0.00000 0.00000 21 0.00000 0.00000 -2.00000 22 0.187500 -0.176159E-13 23 0.250000 -0.697675E-14 -2.00000 24 0.187500 -0.130314E-13 25 0.00000 0.00000 -2.00000 26 -0.00000 0.00000 27 0.187500 0.129965E-14 28 0.250000 -0.108017E-13 29 0.187500 -0.145650E-13 30 0.00000 0.00000 31 0.00000 0.00000 -3.00000 32 0.187500 0.870520E-14 33 0.250000 0.126876E-16 -3.00000 34 0.187500 -0.119192E-14 35 0.00000 0.00000 -3.00000 36 -0.166533E-15 0.00000 37 0.187500 0.475401E-14 38 0.250000 0.163831E-14 39 0.187500 0.156009E-14 40 0.00000 0.00000 41 0.00000 0.00000 -4.00000 42 0.187500 -0.118664E-14 43 0.250000 0.571118E-15 -4.00000 44 0.187500 0.971223E-15 45 0.00000 0.00000 -4.00000 46 0.333067E-15 0.00000 47 0.187500 -0.118535E-14 48 0.250000 0.173997E-15 49 0.187500 0.252876E-15 50 0.00000 0.00000 51 0.00000 0.00000 -5.00000 52 0.187500 0.393546E-16 53 0.250000 -0.761406E-16 -5.00000 54 0.187500 -0.207262E-15 55 0.00000 0.00000 -5.00000 56 -0.00000 0.00000 57 0.187500 0.293579E-15 58 0.250000 -0.00000 59 0.187500 -0.240856E-16 60 0.00000 0.00000 61 0.00000 0.00000 -6.00000 62 0.187500 0.281224E-15 63 0.250000 0.113480E-15 -6.00000 64 0.187500 0.237551E-15 65 0.00000 0.00000 -6.00000 Navier Stokes pressures written to "pressure3.txt". Navier Stokes velocities written to "velocity6.txt". FREE_FEM_NAVIER_STOKES: Normal end of execution. 28 December 2010 10:01:42.516 AM