-- FreeFem++ v4.6 (Thu Apr 2 15:47:38 CEST 2020 - git v4.6) Load: lg_fem lg_mesh lg_mesh3 eigenvalue 1 : // thermal_convection.edp 2 : // 3 : // Discussion: 4 : // 5 : // Forced + Natural heat convection in a pipe 6 : // Navier−Stokes equations + convection−diffusion on temperature 7 : // 8 : // Location: 9 : // 10 : // http://people.sc.fsu.edu/~jburkardt/freefem_src/thermal_convection/thermal_convection.edp 11 : // 12 : // Modified: 13 : // 14 : // 26 June 2015 15 : // 16 : // Author: 17 : // 18 : // Florian De Vuyst 19 : // 20 : // Reference: 21 : // 22 : // Florian De Vuyst, 23 : // Numerical modeling of transport problems using freefem++ software - 24 : // with examples in biology, CFD, traffic flow and energy transfer, 25 : // HAL id: cel-00842234 26 : // https://cel.archives-ouvertes.fr/cel-00842234 27 : // 28 : cout << "\n"; 29 : cout << "thermal_convection:\n"; 30 : cout << " FreeFem++ version\n"; 31 : cout << " Thermal convection and diffusion by Navier-Stok ... : es flow.\n"; 32 : // 33 : // Define the boundary lines. 34 : // 35 : real lx = 0.25; 36 : real Lx = 3.0; 37 : real Ly = 1.0; 38 : 39 : border c1 (t=0.0, lx) {x = t; y = 0.0;} 40 : border c2 (t=lx, Lx-lx) {x = t; y = 0.0;} 41 : border c3 (t=Lx-lx,Lx) {x = t; y = 0.0;} 42 : border c4 (t=0.0,Ly) {x = Lx; y = t;} 43 : border c5 (t=Lx,0.0) {x = t; y = Ly;} 44 : border c6 (t=Ly,0.0) {x = 0.0; y = t;} 45 : // 46 : // Define the mesh. 47 : // 48 : mesh Th = buildmesh ( c1(10) + c2(200) + c3(10) + c4(30) + c5(100) + c6(30) ); 49 : // 50 : // Plot the mesh. 51 : // 52 : plot ( Th, wait = 0, ps = "thermal_convection_mesh.ps" ); 53 : // 54 : // Define the finite element spaces: 55 : // UH for velocity fields, 56 : // XH for pressure P, temperature THETA, and specific volume TAU. 57 : // 58 : fespace Uh(Th, P1b ); 59 : Uh u, v, uold, vold, uh, vh; 60 : fespace Xh(Th, P1 ); 61 : Xh p, ph; 62 : Xh theta, thetaold, thetah; 63 : Xh tau; 64 : // 65 : // Initialize the fields. 66 : // 67 : real uin0 = 0.2; 68 : func uin = uin0 * 4.0 * (y/Ly) * (1.0-y/Ly); 69 : u = uin; 70 : uold = u; 71 : v = 0.0; 72 : vold = v; 73 : 74 : real thetain = 20.0; 75 : theta = thetain; 76 : thetaold = theta; 77 : // 78 : // Define the weak form of the heat equation. 79 : // 80 : real dt = 0.05; 81 : real heatflux = 100.0; 82 : real kappa = 0.001; 83 : 84 : problem HeatStep ( theta, thetah ) = 85 : int2d (Th) ( theta * thetah / dt ) 86 : - int2d (Th) ( convect ([u,v], -dt, thetaold)*thetah/dt ) 87 : + int2d (Th) ( kappa * dx(theta) * dx(thetah) + kappa * dy(theta) * dy(thetah) ) 88 : - int1d (Th, c2) ( kappa * heatflux * thetah ) 89 : + on ( c6, theta = thetain ); 90 : // 91 : // Define the weak form of the Navier Stokes equations. 92 : // 93 : real gravity = 9.81; 94 : real nu = 0.001; 95 : 96 : problem NavierStokesStep ( [u, v, p], [uh, vh, ph] ) = 97 : int2d (Th) ( u * uh / dt ) 98 : - int2d (Th) ( convect ( [uold, vold], -dt, uold ) * uh/dt ) 99 : + int2d (Th) ( nu * dx(u) * dx(uh) + nu * dy(u) * dy(uh) ) 100 : + int2d (Th) ( tau * dx(p) * uh ) 101 : + int2d (Th) ( v * vh / dt ) 102 : - int2d (Th) ( convect ([uold, vold], -dt, vold) * vh / dt ) 103 : + int2d (Th) ( nu * dx(v) * dx(vh) + nu * dy(v) * dy(vh) ) 104 : + int2d (Th) ( tau * dy(p) * vh ) 105 : + int2d (Th) ( gravity * vh ) 106 : + int2d (Th) ( dx(u) * ph + dy(v) * ph ) 107 : + on ( c6, u=uin, v=0 ) 108 : + on ( c1, c2, c3, c5, u=0, v=0 ); 109 : // 110 : // Time steps 111 : // 112 : real cst = 1.0; 113 : real dtsnap = 0.5; 114 : real t = 0.0; 115 : real ttosnap = 2.0; 116 : 117 : for ( int it = 1; it <= 100; it++ ) 118 : { 119 : t = it * dt; 120 : cout << it << " T = " << t << "\n"; 121 : 122 : HeatStep; 123 : 124 : thetaold = theta; 125 : tau = cst * theta; 126 : 127 : NavierStokesStep; 128 : 129 : uold = u; 130 : vold = v; 131 : 132 : plot ( [ u, v ], theta, nbiso = 80, value = 0 ); 133 : 134 : if ( ttosnap <= t ) 135 : { 136 : cout << " Plotting T = " << t << "\n"; 137 : ttosnap = ttosnap + dtsnap; 138 : plot ( [u,v], theta, nbiso = 80, value=0, ps="thermal_convection_"+it+".ps", 139 : cmm="Step "+it ); 140 : } 141 : } 142 : // 143 : // Terminate. 144 : // 145 : cout << "\n"; 146 : cout << "thermal_convection:\n"; 147 : cout << " Normal end of execution.\n"; 148 : 149 : sizestack + 1024 =7024 ( 6000 ) thermal_convection: FreeFem++ version Thermal convection and diffusion by Navier-Stokes flow. -- mesh: Nb of Triangles = 15176, Nb of Vertices 7779 1 T = 0.05 -- Solve : min 19.9863 max 20.697 -- Solve : min -0.00095654 max 0.202809 min -0.0357512 max 0.0343257 min -2.8646e+10 max -2.8646e+10 2 T = 0.1 -- Solve : min 19.9961 max 21.0788 -- Solve : min -0.000797829 max 0.208328 min -0.0684689 max 0.0517979 min -2.26043e+10 max -2.26043e+10 3 T = 0.15 -- Solve : min 19.9969 max 21.3532 -- Solve : min -0.00291817 max 0.242989 min -0.138559 max 0.150182 min -4.37237e+10 max -4.37237e+10 4 T = 0.2 -- Solve : min 19.9975 max 21.577 -- Solve : min -2.53775e-35 max 0.213516 min -0.0507754 max 0.0610707 min 8.1765e+10 max 8.1765e+10 5 T = 0.25 -- Solve : min 19.9989 max 21.771 -- Solve : min -7.81704 max 2.14247 min -12.5495 max 4.57826 min 7.57037e+11 max 7.57037e+11 6 T = 0.3 -- Solve : min 19.9987 max 21.969 -- Solve : min -0.815266 max 0.631163 min -2.71711 max 1.03463 min 4.93962e+11 max 4.93962e+11 7 T = 0.35 -- Solve : min 19.9984 max 22.1258 -- Solve : min -6.66754 max 1.39715 min -10.6608 max 2.79553 min -1.86655e+12 max -1.86655e+12 8 T = 0.4 -- Solve : min 19.9984 max 22.2925 -- Solve : min -0.273551 max 0.535441 min -0.869632 max 1.07398 min 4.067e+11 max 4.067e+11 9 T = 0.45 -- Solve : min 19.9993 max 22.4178 -- Solve : min -0.109551 max 0.338248 min -0.265687 max 0.285058 min -1.12529e+11 max -1.12529e+11 10 T = 0.5 -- Solve : min 19.9997 max 22.5526 -- Solve : min -0.0649077 max 0.335339 min -0.177458 max 0.347726 min -6.8308e+10 max -6.8308e+10 11 T = 0.55 -- Solve : min 19.9997 max 22.6845 -- Solve : min -0.0492551 max 0.270937 min -0.191331 max 0.205879 min 7.62378e+10 max 7.62378e+10 12 T = 0.6 -- Solve : min 19.9998 max 22.8162 -- Solve : min -0.0405175 max 0.265174 min -0.117745 max 0.184585 min -1.15666e+10 max -1.15666e+10 13 T = 0.65 -- Solve : min 19.9998 max 22.9389 -- Solve : min -0.0337485 max 0.259067 min -0.104722 max 0.170016 min -1.71325e+10 max -1.71325e+10 14 T = 0.7 -- Solve : min 19.9999 max 23.0548 -- Solve : min -0.0313949 max 0.275066 min -0.180339 max 0.17975 min -7.47711e+10 max -7.47711e+10 15 T = 0.75 -- Solve : min 19.9999 max 23.1655 -- Solve : min -0.0280628 max 0.303332 min -0.142474 max 0.143105 min -6.28509e+10 max -6.28509e+10 16 T = 0.8 -- Solve : min 19.9999 max 23.2752 -- Solve : min -0.0244289 max 0.246458 min -0.0723736 max 0.135033 min -2.52322e+10 max -2.52322e+10 17 T = 0.85 -- Solve : min 19.9999 max 23.3854 -- Solve : min -0.0247806 max 0.374919 min -0.165542 max 0.232628 min 1.79541e+11 max 1.79541e+11 18 T = 0.9 -- Solve : min 19.9999 max 23.492 -- Solve : min -0.0189976 max 0.252572 min -0.122035 max 0.122205 min 4.8962e+10 max 4.8962e+10 19 T = 0.95 -- Solve : min 20 max 23.595 -- Solve : min -0.0197169 max 0.239908 min -0.058816 max 0.113645 min -9.84059e+10 max -9.84059e+10 20 T = 1 -- Solve : min 20 max 23.6949 -- Solve : min -0.0238732 max 0.236633 min -0.0466118 max 0.14124 min -2.99268e+10 max -2.99268e+10 21 T = 1.05 -- Solve : min 20 max 23.7921 -- Solve : min -0.0241268 max 0.246496 min -0.0435611 max 0.100722 min -5.21497e+10 max -5.21497e+10 22 T = 1.1 -- Solve : min 20 max 23.887 -- Solve : min -0.0252419 max 0.23279 min -0.0418586 max 0.0970016 min -1.15145e+10 max -1.15145e+10 23 T = 1.15 -- Solve : min 20 max 23.9797 -- Solve : min -0.0340755 max 0.282816 min -0.117112 max 0.120039 min 8.01047e+10 max 8.01047e+10 24 T = 1.2 -- Solve : min 20 max 24.0705 -- Solve : min -0.0317914 max 0.229487 min -0.048611 max 0.0881984 min 1.90579e+10 max 1.90579e+10 25 T = 1.25 -- Solve : min 20 max 24.1593 -- Solve : min -0.0331064 max 0.228655 min -0.0718335 max 0.0861925 min -3.88006e+10 max -3.88006e+10 26 T = 1.3 -- Solve : min 20 max 24.2467 -- Solve : min -0.0350191 max 0.298622 min -0.110575 max 0.30801 min -9.07942e+10 max -9.07942e+10 27 T = 1.35 -- Solve : min 20 max 24.3332 -- Solve : min -8.68661 max 7.85343 min -5.95366 max 7.65562 min 1.89046e+12 max 1.89046e+12 28 T = 1.4 -- Solve : min 20 max 24.4023 -- Solve : min -3.27809 max 1.58706 min -7.8978 max 7.60643 min 2.71711e+12 max 2.71711e+12 29 T = 1.45 -- Solve : min 19.9999 max 24.4791 -- Solve : min -0.48751 max 0.555937 min -1.35839 max 0.721404 min -1.02078e+12 max -1.02078e+12 30 T = 1.5 -- Solve : min 20 max 24.5645 -- Solve : min -0.164092 max 0.393625 min -0.29158 max 0.304981 min -1.28655e+11 max -1.28655e+11 31 T = 1.55 -- Solve : min 20 max 24.6591 -- Solve : min -0.114993 max 0.335953 min -0.276263 max 0.23925 min -8.56314e+10 max -8.56314e+10 32 T = 1.6 -- Solve : min 20 max 24.7503 -- Solve : min -0.0949953 max 0.31649 min -0.171929 max 0.194762 min -1.56213e+10 max -1.56213e+10 33 T = 1.65 -- Solve : min 20 max 24.8349 -- Solve : min -0.0865417 max 0.300314 min -0.152646 max 0.16557 min 2.60131e+10 max 2.60131e+10 34 T = 1.7 -- Solve : min 20 max 24.9154 -- Solve : min -0.0814275 max 0.29364 min -0.130956 max 0.146246 min -1.42393e+10 max -1.42393e+10 35 T = 1.75 -- Solve : min 20 max 24.9936 -- Solve : min -0.0784467 max 0.281307 min -0.116785 max 0.133161 min -3.60515e+09 max -3.60515e+09 36 T = 1.8 -- Solve : min 20 max 25.0708 -- Solve : min -0.07688 max 0.269394 min -0.103234 max 0.121207 min -1.10615e+10 max -1.10615e+10 37 T = 1.85 -- Solve : min 20 max 25.1474 -- Solve : min -0.0792421 max 0.263417 min -0.0966602 max 0.113523 min -5.55518e+10 max -5.55518e+10 38 T = 1.9 -- Solve : min 20 max 25.2241 -- Solve : min -0.0793047 max 0.257201 min -0.0899844 max 0.106711 min -1.59727e+10 max -1.59727e+10 39 T = 1.95 -- Solve : min 20 max 25.3011 -- Solve : min -0.0883918 max 0.266544 min -0.166876 max 0.208387 min 1.92982e+11 max 1.92982e+11 40 T = 2 -- Solve : min 20 max 25.3781 -- Solve : min -0.083905 max 0.294479 min -0.132148 max 0.38842 min 1.22171e+11 max 1.22171e+11 Plotting T = 2 41 T = 2.05 -- Solve : min 20 max 25.4558 -- Solve : min -0.0837239 max 0.236086 min -0.0700076 max 0.106608 min -1.09933e+10 max -1.09933e+10 42 T = 2.1 -- Solve : min 20 max 25.5352 -- Solve : min -0.388488 max 0.671075 min -1.72953 max 0.773078 min 2.18874e+11 max 2.18874e+11 43 T = 2.15 -- Solve : min 20 max 25.6171 -- Solve : min -0.0895998 max 0.230357 min -0.168748 max 0.129978 min -1.29422e+10 max -1.29422e+10 44 T = 2.2 -- Solve : min 20 max 25.6986 -- Solve : min -0.0890896 max 0.227236 min -0.108703 max 0.110481 min 2.06017e+10 max 2.06017e+10 45 T = 2.25 -- Solve : min 20 max 25.7803 -- Solve : min -0.0931741 max 0.226117 min -0.0687781 max 0.116862 min -4.25719e+09 max -4.25719e+09 46 T = 2.3 -- Solve : min 20 max 25.8625 -- Solve : min -0.0981722 max 0.224007 min -0.0615559 max 0.123855 min -1.68179e+10 max -1.68179e+10 47 T = 2.35 -- Solve : min 20 max 25.9452 -- Solve : min -0.106502 max 0.223609 min -0.0518395 max 0.133212 min -6.88393e+10 max -6.88393e+10 48 T = 2.4 -- Solve : min 20 max 26.0282 -- Solve : min -0.113892 max 0.224042 min -0.0536817 max 0.139805 min -2.08306e+10 max -2.08306e+10 49 T = 2.45 -- Solve : min 20 max 26.1111 -- Solve : min -0.108139 max 0.456179 min -0.180008 max 0.762363 min -2.8673e+11 max -2.8673e+11 50 T = 2.5 -- Solve : min 20 max 26.1941 -- Solve : min -0.11835 max 0.225694 min -0.0652039 max 0.158629 min 5.46789e+09 max 5.46789e+09 Plotting T = 2.5 51 T = 2.55 -- Solve : min 20 max 26.2749 -- Solve : min -0.131188 max 0.223579 min -0.0773967 max 0.170791 min -7.05758e+10 max -7.05758e+10 52 T = 2.6 -- Solve : min 20 max 26.3548 -- Solve : min -0.139164 max 0.22391 min -0.0716091 max 0.177518 min 2.65531e+10 max 2.65531e+10 53 T = 2.65 -- Solve : min 20 max 26.4333 -- Solve : min -0.148692 max 0.223737 min -0.0762462 max 0.184652 min -2.74318e+10 max -2.74318e+10 54 T = 2.7 -- Solve : min 20 max 26.5136 -- Solve : min -0.155651 max 0.223353 min -0.0810851 max 0.199378 min -1.6949e+10 max -1.6949e+10 55 T = 2.75 -- Solve : min 20 max 26.6032 -- Solve : min -0.161609 max 0.223064 min -0.0860197 max 0.211439 min 2.27401e+10 max 2.27401e+10 56 T = 2.8 -- Solve : min 20 max 26.6906 -- Solve : min -0.169599 max 0.222637 min -0.0910697 max 0.224105 min -1.1302e+10 max -1.1302e+10 57 T = 2.85 -- Solve : min 20 max 26.7755 -- Solve : min -0.368622 max 0.512693 min -0.455179 max 1.12088 min 2.35905e+11 max 2.35905e+11 58 T = 2.9 -- Solve : min 20 max 26.8547 -- Solve : min -0.201048 max 0.254172 min -0.102216 max 0.250057 min 5.09048e+10 max 5.09048e+10 59 T = 2.95 -- Solve : min 20 max 26.9489 -- Solve : min -0.197664 max 0.24346 min -0.108982 max 0.262727 min -4.64063e+10 max -4.64063e+10 60 T = 3 -- Solve : min 20 max 27.0389 -- Solve : min -0.197448 max 0.249827 min -0.161199 max 0.274209 min -4.24233e+10 max -4.24233e+10 Plotting T = 3 61 T = 3.05 -- Solve : min 20 max 27.1244 -- Solve : min -1.43143 max 3.15333 min -3.48504 max 1.9442 min -1.79826e+12 max -1.79826e+12 62 T = 3.1 -- Solve : min 20 max 27.2041 -- Solve : min -2.19381 max 1.72807 min -4.46802 max 2.4445 min 2.90183e+12 max 2.90183e+12 63 T = 3.15 -- Solve : min 20 max 27.2589 -- Solve : min -10.4854 max 4.52107 min -6.93926 max 5.97492 min 3.62175e+12 max 3.62175e+12 64 T = 3.2 -- Solve : min 19.9999 max 27.3138 -- Solve : min -0.906351 max 1.49839 min -2.51383 max 2.78046 min -9.62669e+11 max -9.62669e+11 65 T = 3.25 -- Solve : min 19.9999 max 27.3505 -- Solve : min -6.473 max 4.23851 min -4.90755 max 11.7163 min 6.01761e+12 max 6.01761e+12 66 T = 3.3 -- Solve : min 19.9998 max 27.3902 -- Solve : min -0.741366 max 1.94087 min -1.04017 max 1.54191 min 1.09516e+12 max 1.09516e+12 67 T = 3.35 -- Solve : min 19.9997 max 27.4359 -- Solve : min -0.220947 max 0.558515 min -0.601781 max 0.409764 min 1.84325e+11 max 1.84325e+11 68 T = 3.4 -- Solve : min 19.9994 max 27.4583 -- Solve : min -0.328335 max 0.835724 min -0.860809 max 0.43949 min -1.2341e+11 max -1.2341e+11 69 T = 3.45 -- Solve : min 19.9991 max 27.4578 -- Solve : min -0.299035 max 0.403698 min -0.374993 max 0.460487 min 1.45962e+10 max 1.45962e+10 70 T = 3.5 -- Solve : min 19.998 max 27.4857 -- Solve : min -0.284121 max 0.382889 min -0.328497 max 0.48369 min -2.33149e+09 max -2.33149e+09 Plotting T = 3.5 71 T = 3.55 -- Solve : min 19.9963 max 27.5446 -- Solve : min -0.278488 max 0.356975 min -0.296016 max 0.508084 min -1.65476e+10 max -1.65476e+10 72 T = 3.6 -- Solve : min 19.9951 max 27.516 -- Solve : min -0.276911 max 0.341294 min -0.279419 max 0.522856 min 1.66899e+10 max 1.66899e+10 73 T = 3.65 -- Solve : min 19.9959 max 27.5844 -- Solve : min -0.274301 max 0.328605 min -0.2651 max 0.543076 min 2.02613e+10 max 2.02613e+10 74 T = 3.7 -- Solve : min 19.9961 max 27.5881 -- Solve : min -0.347606 max 0.604811 min -1.75382 max 0.984186 min 3.49225e+11 max 3.49225e+11 75 T = 3.75 -- Solve : min 19.9973 max 27.6264 -- Solve : min -0.312775 max 0.330595 min -0.247431 max 0.565185 min -3.90126e+10 max -3.90126e+10 76 T = 3.8 -- Solve : min 19.9963 max 27.6465 -- Solve : min -0.296909 max 0.349517 min -0.242675 max 0.572433 min 1.23175e+10 max 1.23175e+10 77 T = 3.85 -- Solve : min 19.9957 max 27.6969 -- Solve : min -0.295189 max 0.360827 min -0.241614 max 0.589221 min -2.78957e+10 max -2.78957e+10 78 T = 3.9 -- Solve : min 19.9964 max 27.7392 -- Solve : min -0.289085 max 0.371463 min -0.243578 max 0.598711 min -1.50256e+11 max -1.50256e+11 79 T = 3.95 -- Solve : min 19.9979 max 27.7714 -- Solve : min -0.291887 max 0.385058 min -0.238617 max 0.601056 min 9.5898e+10 max 9.5898e+10 80 T = 4 -- Solve : min 19.9973 max 27.7915 -- Solve : min -0.30925 max 0.382352 min -0.409511 max 0.626931 min 2.39419e+11 max 2.39419e+11 Plotting T = 4 81 T = 4.05 -- Solve : min 19.9956 max 27.7971 -- Solve : min -0.348853 max 0.401224 min -0.599881 max 0.642617 min -1.27536e+11 max -1.27536e+11 82 T = 4.1 -- Solve : min 19.9945 max 27.8246 -- Solve : min -0.297422 max 0.414477 min -0.615806 max 0.650265 min 3.10122e+11 max 3.10122e+11 83 T = 4.15 -- Solve : min 19.9944 max 27.8571 -- Solve : min -0.294676 max 0.410314 min -0.259127 max 0.66834 min -1.89592e+10 max -1.89592e+10 84 T = 4.2 -- Solve : min 19.9943 max 27.8716 -- Solve : min -0.295508 max 0.407623 min -0.262498 max 0.683126 min -3.42656e+10 max -3.42656e+10 85 T = 4.25 -- Solve : min 19.9947 max 27.8914 -- Solve : min -0.302875 max 0.406631 min -0.265717 max 0.695358 min 4.11373e+10 max 4.11373e+10 86 T = 4.3 -- Solve : min 19.9934 max 27.8443 -- Solve : min -0.307055 max 0.411437 min -0.272499 max 0.719606 min 6.20068e+10 max 6.20068e+10 87 T = 4.35 -- Solve : min 19.9936 max 27.8686 -- Solve : min -0.310666 max 0.415905 min -0.282273 max 0.725339 min 3.82566e+10 max 3.82566e+10 88 T = 4.4 -- Solve : min 19.9938 max 27.8249 -- Solve : min -0.308674 max 0.412399 min -0.323264 max 0.739488 min -8.82458e+10 max -8.82458e+10 89 T = 4.45 -- Solve : min 19.9943 max 27.7553 -- Solve : min -0.30364 max 0.413063 min -0.303753 max 0.752047 min -3.29734e+10 max -3.29734e+10 90 T = 4.5 -- Solve : min 19.9953 max 27.7474 -- Solve : min -0.297511 max 0.411489 min -0.313709 max 0.760976 min -1.92659e+10 max -1.92659e+10 Plotting T = 4.5 91 T = 4.55 -- Solve : min 19.9964 max 27.7575 -- Solve : min -0.287198 max 0.411409 min -0.325314 max 0.768204 min -2.61149e+10 max -2.61149e+10 92 T = 4.6 -- Solve : min 19.9927 max 27.7584 -- Solve : min -0.274955 max 0.546477 min -0.85277 max 0.78357 min 2.10924e+11 max 2.10924e+11 93 T = 4.65 -- Solve : min 19.9915 max 27.7525 -- Solve : min -0.269125 max 0.420236 min -0.363076 max 0.780972 min -5.88101e+10 max -5.88101e+10 94 T = 4.7 -- Solve : min 19.9945 max 27.7718 -- Solve : min -0.251477 max 0.42493 min -0.42843 max 0.768545 min 1.57686e+11 max 1.57686e+11 95 T = 4.75 -- Solve : min 19.9963 max 27.8134 -- Solve : min -0.244811 max 0.429697 min -0.372598 max 0.775848 min 2.02892e+09 max 2.02892e+09 96 T = 4.8 -- Solve : min 19.996 max 27.8689 -- Solve : min -0.250751 max 0.436159 min -0.382712 max 0.760797 min -2.8979e+10 max -2.8979e+10 97 T = 4.85 -- Solve : min 19.9956 max 27.9302 -- Solve : min -0.256894 max 0.436837 min -0.392767 max 0.78997 min 2.44234e+10 max 2.44234e+10 98 T = 4.9 -- Solve : min 19.9955 max 27.9736 -- Solve : min -0.262604 max 0.442567 min -0.402424 max 0.817015 min -1.4785e+10 max -1.4785e+10 99 T = 4.95 -- Solve : min 19.9944 max 27.9562 -- Solve : min -0.270995 max 0.444201 min -0.447252 max 0.832176 min 4.04291e+10 max 4.04291e+10 100 T = 5 -- Solve : min 19.9924 max 27.8464 -- Solve : min -0.274214 max 0.448303 min -0.419693 max 0.845348 min 8.36336e+09 max 8.36336e+09 Plotting T = 5 thermal_convection: Normal end of execution. times: compile 0.005612s, execution 800.688s, mpirank:0 CodeAlloc : nb ptr 4097, size :506096 mpirank: 0 Ok: Normal End