-- FreeFem++ v4.6 (Thu Apr  2 15:47:38 CEST 2020 - git v4.6)
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  Discussion:
    2 : //
    3 : //    Vortex caused by free convection
    4 : //
    5 : //    Solves the Laplace Equation on a parallel plate capacitor boundary.
    6 : //    P1 Elements are used.
    7 : //
    8 : //    Export the data, using ffmatlib, for graphic processing by MATLAB or Octave.
    9 : //
   10 : //  Licensing:
   11 : //
   12 : //    Copyright (C) 2018 Chloros2 <chloros2@gmx.de>
   13 : //
   14 : //    This program is free software: you can redistribute it and/or modify it
   15 : //    under the terms of the GNU General Public License as published by
   16 : //    the Free Software Foundation, either version 3 of the License, or
   17 : //    (at your option) any later version.
   18 : //
   19 : //    This program is distributed in the hope that it will be useful, but
   20 : //    WITHOUT ANY WARRANTY; without even the implied warranty of
   21 : //    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   22 : //    GNU General Public License for more details.
   23 : //
   24 : //    You should have received a copy of the GNU General Public License
   25 : //    along with this program.  If not, see
   26 : //    <https://www.gnu.org/licenses/>.
   27 : //
   28 : //  Modified:
   29 : //
   30 : //    2018-05-19
   31 : //
   32 : // Author: 
   33 : //
   34 : //   Chloros2 <chloros2@gmx.de>
   35 : //
   36 : //  Local:
   37 : //
   38 : //    real dt, the time step.
   39 : //
   40 : //    real g, gravitational coefficient.
   41 : //
   42 : //    real Tcold, the temperature of the cold wall, in centigrade.
   43 : //
   44 : //    real tend, the final time.
   45 : //
   46 : //    real Thot, the temperature of the hot wall, in centigrade.
   47 : //
   48 : include "ffmatlib.idp"/*ffmatlib.idp Export Macros (Plot Solutions for Matlab and Octave)
    2 :  *
    3 :  * Author: Chloros2 <chloros2@gmx.de>
    4 :  * Created: 2018-12-21
    5 :  *
    6 :  *   This file is part of the ffmatlib which is hosted at
    7 :  *   https://github.com/samplemaker/freefem_matlab_octave_plot
    8 :  *
    9 :  * Copyright (C) 2018 Chloros2 <chloros2@gmx.de>
   10 :  *
   11 :  * This program is free software: you can redistribute it and/or modify it
   12 :  * under the terms of the GNU General Public License as published by
   13 :  * the Free Software Foundation, either version 3 of the License, or
   14 :  * (at your option) any later version.
   15 :  *
   16 :  * This program is distributed in the hope that it will be useful, but
   17 :  * WITHOUT ANY WARRANTY; without even the implied warranty of
   18 :  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   19 :  * GNU General Public License for more details.
   20 :  *
   21 :  * You should have received a copy of the GNU General Public License
   22 :  * along with this program.  If not, see
   23 :  * <https://www.gnu.org/licenses/>.
   24 :  *
   25 :  */
   26 : 
   27 : //Save finite element connectivity (j-th degree of freedom for i-th element)
   28 : macro ffSaveVh(Th, Vh, filename){
   29 #   {
   30 #   ofstream file(filename);
   31 #   file.precision(10);
   32 #   for (int i=0; i<Th.nt; i++){
   33 #     for (int j=0; j<Vh.ndofK; j++){
   34 #       file << Vh(i,j) << "\n";
   35 #     }
   36 #   }
   37 #   }
   38 # }  )  //EOM
   39 : 
   40 : //Save FE Space data
   41 : macro ffSaveData(u, filename){
   42 #   {
   43 #   ofstream file(filename);
   44 #   file.precision(10);
   45 #   for (int j=0; j<u[].n; j++){
   46 #     file << u[][j] << endl;
   47 #   }
   48 #   }
   49 # }  )  //EOM
   50 : 
   51 : macro ffSaveData2(u1, u2, filename){
   52 #   {
   53 #   ofstream file(filename);
   54 #   int datalen=u1[].n;
   55 #   if (u2[].n!=datalen){
   56 #     cout << "error: arguments must have same size" << endl;
   57 #     exit(1);
   58 #   }
   59 #   file.precision(10);
   60 #   for (int j=0; j<datalen; j++){
   61 #     file << u1[][j] << " " << u2[][j] << endl;
   62 #   }
   63 #   }
   64 # }  )  //EOM
   65 : 
   66 : macro ffSaveData3(u1, u2, u3, filename){
   67 #   {
   68 #   ofstream file(filename);
   69 #   int datalen=u1[].n;
   70 #   if ((u2[].n!=datalen) | (u3[].n!=datalen)){
   71 #     cout << "error: arguments must have same size" << endl;
   72 #     exit(1);
   73 #   }
   74 #   file.precision(10);
   75 #   for (int j=0; j<datalen; j++){
   76 #     file << u1[][j] << " " << u2[][j] << " " << u3[][j] << endl;
   77 #   }
   78 #   }
   79 # }  )  //EOM
   80 : 
   81 : macro ffSaveData4(u1, u2, u3, u4, filename){
   82 #   {
   83 #   ofstream file(filename);
   84 #   int datalen=u1[].n;
   85 #   if ((u2[].n!=datalen) | (u3[].n!=datalen) | (u4[].n!=datalen)){
   86 #     cout << "error: arguments must have same size" << endl;
   87 #     exit(1);
   88 #   }
   89 #   file.precision(10);
   90 #   for (int j=0; j<datalen; j++){
   91 #     file << u1[][j] << " " << u2[][j] << " " << u3[][j] << " " << u4[][j] << endl;
   92 #   }
   93 #   }
   94 # }  )  //EOM
   95 : 
   49 : 
   50 : load "UMFPACK64";
   51 : 
   52 : cout << endl;
   53 : cout << "convective_rolls:" << endl;
   54 : cout << "  FreeFem++ version." << endl;
   55 : cout << "  Solve the Laplace equation on a parallel plate 
  ... : capacitor boundary." << endl;
   56 : cout << "  Record data about the resulting convective roll
  ... : s." << endl;
   57 : cout << "  Using the ffmatlib interface, export the data f
  ... : or graphic" << endl;
   58 : cout << "  processing by MATLAB/Octave." << endl;
   59 : //
   60 : //  Geometry.
   61 : //
   62 : real width = 0.30;
   63 : real height = 0.05;
   64 : 
   65 : int m = 300;
   66 : 
   67 : real tend=5.0;
   68 : real dt=0.04;
   69 : //
   70 : //  Set physical parameters.
   71 : //
   72 : real g = 9.81;
   73 : real Thot = 50.0;
   74 : real Tcold = 0.0;
   75 : real beta = (1.0/(273.0+0.5*(Thot+Tcold)));  // Expansion coefficient
   76 : //properties air @25°C / 1 bar
   77 : real rho = 1.168;         // density kg/m^3
   78 : real nu = 15.82e-6;       // kinematic viscosity m^2/s
   79 : real cp = 1.007e+3;       // specific isobar heat capacity J/kg*K
   80 : real lambda = 0.0261;     // heat conductivity W/mK
   81 : real mu = nu * rho;
   82 : real a = lambda / ( rho * cp );
   83 : //
   84 : //  Define the boundaries of the region.
   85 : //
   86 : int C1=1;
   87 : int C2=2;
   88 : int C3=3;
   89 : int C4=4;
   90 : int C10=5;
   91 : border floor(t=0,width){ x=t; y=0; label=C1;}
 *** Warning  The identifier floor hide a Global identifier  
;
   92 : border ceiling(t=width,0){ x=t; y=height; label=C2;};
   93 : border right(t=0,height){ x=width; y=t; label=C3;};
   94 : border left(t=height,0){ x=0; y=t; label=C4;};
   95 : //
   96 : //  Create the mesh.
   97 : //
   98 : mesh Th = buildmesh ( 
   99 :     floor ( width * m )
  100 :   + right ( height * m )
  101 :   + ceiling ( width * m )
  102 :   + left ( height * m ) );
  103 : //
  104 : //  Plot the mesh.
  105 : //
  106 : plot ( Th, wait = false,
  107 :   ps = "convective_rolls_mesh.ps" );
  108 : //
  109 : //  Set finite element spaces for velocity and pressure.
  110 : //
  111 : fespace Vh ( Th, P2 );
  112 : fespace Qh ( Th, P1 );
  113 : //
  114 : //Fluid stuff
  115 : //
  116 : Vh u1,u2,v2,v1,up=0,vp=0;
  117 : Qh p=0, pp;
  118 : Qh psi,phi;
  119 : //
  120 : //r is a temperature rise/difference
  121 : //
  122 : Qh rr, rp=0,r=0;
  123 : Qh Tfluid;
  124 : //Heatflux density
  125 : Qh qx, qy;
  126 : 
  127 : bool reuseMatrix=false;
  128 : int n=0;
  129 : //
  130 : //  Define Navier Stokes problem for velocity and pressure.
  131 : //
  132 : problem NS([u1,u2,p],[v1,v2,pp],solver=UMFPACK, init=reuseMatrix) =
  133 :       int2d(Th)( u1*v1 + u2*v2                //Remains from advective part in lagrange coordinates
  134 :                  + nu*dt*(dx(u1)*dx(v1) + dy(u1)*dy(v1)   //Viscous part
  135 :                  +        dx(u2)*dx(v2) + dy(u2)*dy(v2))
  136 :                  + p*pp*1.e-6                             //Stabilization
  137 :                  - dt*(p*(dx(v1) + dy(v2))/rho            //Pressure part
  138 :                  - dt*pp*(dx(u1) + dy(u2))))              //Mass conservation (continuity)
  139 :      - int2d(Th) (convect([up,vp],-dt,up)*v1              //Advection Lagrangian coordinates
  140 :                  + convect([up,vp],-dt,vp)*v2
  141 :                  + dt*beta*g*r*v2)                        //Buyoancy
  142 : 
  143 :       + on(C1,C2,C3,C4,u2=0) + on(C1,C2,C3,C4,u1=0);       //no-slip on box surface
  144 : //
  145 : //  Define convection-diffusion problem for heat.
  146 : //
  147 : problem convectdiffusion(r,rr,solver=UMFPACK, init=reuseMatrix) =
  148 :           int2d(Th)( r*rr                       //Remains from advective part in lagrangian coordinates
  149 :                      + a*dt*(dx(r)*dx(rr)+dy(r)*dy(rr)))   //Diffusion part
  150 :         - int2d(Th)(convect([up,vp],-dt,rp)*rr)            //Advection Lagrangian coordinates
  151 :         + on(C2,C3,C4,r=0) + on(C1,r=Thot-Tcold);
  152 : //
  153 : //  in order to calculate the heat transfer coefficient
  154 : //
  155 : Vh o=1;
  156 : real lenfloor = int1d(Th,C1,qfe=qf2pE)(o);
  157 : //
  158 : //  Define problem for stream function.
  159 : //
  160 : problem streamlines(psi,phi) =
  161 :       int2d(Th)( dx(psi)*dx(phi) + dy(psi)*dy(phi))
  162 :    +  int2d(Th)( -phi*(dy(u1) - dx(u2)))
  163 :    +  on(C1,psi=0.);
  164 : 
  165 : cout.precision(3);
  166 : 
  167 : for ( real t = 0.0; t < tend; t = t + dt )
  168 : {
  169 :   NS;
  170 :   up=u1;
  171 :   vp=u2;
  172 : //plot([u1,u2],p,value=1, cmm="t="+t);
  173 :   convectdiffusion;
  174 :   rp=r;
  175 :   plot(r, wait = false, value=false, nbiso=20, fill=true, cmm="Temperature rise r at t="+t);
  176 :   reuseMatrix=true;
  177 :   cout << "Timestamp:		" << t << "sec / " << tend << "sec" << endl;
  178 :   streamlines;
  179 : //plot(psi,nbiso=20, fill=false,value=true,cmm="Streamlines [(m^3/s)/m]; t="+t+"sec; alpha="+alpha+"W/m^2K",wait=0);
  180 :   n=n+1;
  181 : }
  182 : 
  183 : qx = -lambda*dx(r);
  184 : qy = -lambda*dy(r);
  185 : real heatflux = int1d(Th,C1,qfe=qf2pE)(qx*N.x+qy*N.y);
  186 : real alpha = -heatflux/(lenfloor*(Thot-Tcold));
  187 : 
  188 : cout << endl;
  189 : cout << "Heat transfer:		" << heatflux << "W/m" << endl;
  190 : cout << "Heat transfer coef:	" << alpha << "W/m^2K" << endl;
  191 : cout << "Prandtl Number:		" << nu/a << endl;
  192 : cout << "Beta:			" << beta << "1/K" << endl;
  193 : cout << "Thermal diffusivity:	" << a << "m^2/s" << endl;
  194 : cout << endl;
  195 : cout << "NbBoundaryElements:	" << Th.nbe << endl;
  196 : cout << "NbTriangles:		" << Th.nt << endl;
  197 : cout << "NbVertices:		" << Th.nv << endl;
  198 : cout << "nDoF (T & Psi):		" << Qh.ndof << endl;
  199 : cout << "nDoF (u1,u2):		" << Vh.ndof << endl;
  200 : cout << endl;
  201 : 
  202 : Tfluid = r + Tcold;
  203 : //
  204 : //  Write data to files.
  205 : //
  206 : savemesh ( Th, "convective_rolls.msh" );
  207 : ffSaveVh ( Th, Vh, "convective_rolls_vh.txt" )
   29 @   
   30 @    
   31 @   
   32 @       
   33 @         
   34 @           
   35 @     
   36 @   
   37 @   
   38 @  {
   29 @   {
   30 @   ofstream file( "convective_rolls_vh.txt");
   31 @   file.precision(10);
   32 @   for (int i=0; i< Th.nt; i++){
   33 @     for (int j=0; j< Vh.ndofK; j++){
   34 @       file <<  Vh(i,j) << "\n";
   35 @     }
   36 @   }
   37 @   }
   38 @ } ;
  208 : ffSaveVh ( Th, Qh, "convective_rolls_qh.txt" )
   29 @   
   30 @    
   31 @   
   32 @       
   33 @         
   34 @           
   35 @     
   36 @   
   37 @   
   38 @  {
   29 @   {
   30 @   ofstream file( "convective_rolls_qh.txt");
   31 @   file.precision(10);
   32 @   for (int i=0; i< Th.nt; i++){
   33 @     for (int j=0; j< Qh.ndofK; j++){
   34 @       file <<  Qh(i,j) << "\n";
   35 @     }
   36 @   }
   37 @   }
   38 @ } ;
  209 : ffSaveData ( psi, "convective_rolls_psi.txt" )
   42 @   
   43 @    
   44 @   
   45 @       
   46 @         
   47 @   
   48 @   
   49 @  {
   42 @   {
   43 @   ofstream file( "convective_rolls_psi.txt");
   44 @   file.precision(10);
   45 @   for (int j=0; j< psi[].n; j++){
   46 @     file <<  psi[][j] << endl;
   47 @   }
   48 @   }
   49 @ } ;
  210 : ffSaveData ( Tfluid, "convective_rolls_temperature.txt" )
   42 @   
   43 @    
   44 @   
   45 @       
   46 @         
   47 @   
   48 @   
   49 @  {
   42 @   {
   43 @   ofstream file( "convective_rolls_temperature.txt");
   44 @   file.precision(10);
   45 @   for (int j=0; j< Tfluid[].n; j++){
   46 @     file <<  Tfluid[][j] << endl;
   47 @   }
   48 @   }
   49 @ } ;
  211 : ffSaveData2 ( u1, u2, "convective_rolls_ux_uy.txt" )
   52 @   
   53 @    
   54 @    
   55 @    
   56 @         
   57 @     
   58 @   
   59 @   
   60 @       
   61 @             
   62 @   
   63 @   
   64 @  {
   52 @   {
   53 @   ofstream file( "convective_rolls_ux_uy.txt");
   54 @   int datalen= u1[].n;
   55 @   if ( u2[].n!=datalen){
   56 @     cout << "error: arguments must have same size" << endl;
   57 @     exit(1);
   58 @   }
   59 @   file.precision(10);
   60 @   for (int j=0; j<datalen; j++){
   61 @     file <<  u1[][j] << " " <<  u2[][j] << endl;
   62 @   }
   63 @   }
   64 @ } ;
  212 : //
  213 : //  Terminate.
  214 : //
  215 : cout << "\n";
  216 : cout << "convective_rolls:\n";
  217 : cout << "  Normal end of execution.\n";
  218 : 
  219 : exit ( 0 );
  220 : 
  221 :  sizestack + 1024 =8280  ( 7256 )


convective_rolls:
  FreeFem++ version.
  Solve the Laplace equation on a parallel plate capacitor boundary.
  Record data about the resulting convective rolls.
  Using the ffmatlib interface, export the data for graphic
  processing by MATLAB/Octave.
  --  mesh:  Nb of Triangles =   3170, Nb of Vertices 1691
  -- Solve : 
          min 0  max 0
          min 0  max 0
          min 0  max 0
  -- Solve : 
          min -10.4  max 50
Timestamp:		0sec / 5sec
  -- Solve : 
          min 0  max 0
  -- Solve : 
          min -0.0038  max 0.00527
          min -0.0168  max 0.00521
          min -0.00235  max 0.000793
  -- Solve : 
          min -5.3  max 50
Timestamp:		0.04sec / 5sec
  -- Solve : 
          min -3.31e-06  max 3.03e-06
  -- Solve : 
          min -0.00528  max 0.00706
          min -0.0214  max 0.00664
          min -0.00282  max 0.000719
  -- Solve : 
          min -2.24  max 50
Timestamp:		0.08sec / 5sec
  -- Solve : 
          min -5.2e-06  max 4.7e-06
  -- Solve : 
          min -0.00608  max 0.00739
          min -0.0213  max 0.00665
          min -0.00327  max 0.000614
  -- Solve : 
          min -2.07  max 50
Timestamp:		0.12sec / 5sec
  -- Solve : 
          min -6.48e-06  max 5.77e-06
  -- Solve : 
          min -0.00641  max 0.0072
          min -0.0201  max 0.00643
          min -0.00375  max 0.000494
  -- Solve : 
          min -1.56  max 50
Timestamp:		0.16sec / 5sec
  -- Solve : 
          min -7.6e-06  max 6.68e-06
  -- Solve : 
          min -0.00646  max 0.00686
          min -0.019  max 0.00613
          min -0.00417  max 0.000362
  -- Solve : 
          min -0.922  max 50
Timestamp:		0.2sec / 5sec
  -- Solve : 
          min -8.97e-06  max 7.59e-06
  -- Solve : 
          min -0.00636  max 0.00651
          min -0.0181  max 0.0065
          min -0.00456  max 0.000336
  -- Solve : 
          min -0.553  max 50
Timestamp:		0.24sec / 5sec
  -- Solve : 
          min -1.09e-05  max 8.87e-06
  -- Solve : 
          min -0.00618  max 0.0062
          min -0.0176  max 0.00718
          min -0.00494  max 0.000335
  -- Solve : 
          min -0.469  max 50
Timestamp:		0.28sec / 5sec
  -- Solve : 
          min -1.31e-05  max 1.09e-05
  -- Solve : 
          min -0.00597  max 0.00594
          min -0.0173  max 0.00796
          min -0.0053  max 0.000338
  -- Solve : 
          min -0.326  max 50
Timestamp:		0.32sec / 5sec
  -- Solve : 
          min -1.56e-05  max 1.32e-05
  -- Solve : 
          min -0.00667  max 0.00658
          min -0.0172  max 0.00885
          min -0.00564  max 0.000376
  -- Solve : 
          min -0.202  max 50
Timestamp:		0.36sec / 5sec
  -- Solve : 
          min -1.86e-05  max 1.69e-05
  -- Solve : 
          min -0.00787  max 0.00783
          min -0.0174  max 0.00987
          min -0.00601  max 0.000411
  -- Solve : 
          min -0.198  max 50
Timestamp:		0.4sec / 5sec
  -- Solve : 
          min -2.22e-05  max 2.07e-05
  -- Solve : 
          min -0.00914  max 0.00915
          min -0.0177  max 0.011
          min -0.00637  max 0.000443
  -- Solve : 
          min -0.175  max 50
Timestamp:		0.44sec / 5sec
  -- Solve : 
          min -2.65e-05  max 2.47e-05
  -- Solve : 
          min -0.0105  max 0.0105
          min -0.0183  max 0.0123
          min -0.00673  max 0.00048
  -- Solve : 
          min -0.135  max 50
Timestamp:		0.48sec / 5sec
  -- Solve : 
          min -3.18e-05  max 2.88e-05
  -- Solve : 
          min -0.0118  max 0.012
          min -0.0192  max 0.0138
          min -0.00708  max 0.000533
  -- Solve : 
          min -0.0951  max 50
Timestamp:		0.52sec / 5sec
  -- Solve : 
          min -3.81e-05  max 3.31e-05
  -- Solve : 
          min -0.0133  max 0.0135
          min -0.0204  max 0.0155
          min -0.00744  max 0.000591
  -- Solve : 
          min -0.0853  max 50
Timestamp:		0.56sec / 5sec
  -- Solve : 
          min -4.56e-05  max 3.98e-05
  -- Solve : 
          min -0.0148  max 0.0151
          min -0.0229  max 0.0185
          min -0.00779  max 0.000654
  -- Solve : 
          min -0.0813  max 50
Timestamp:		0.6sec / 5sec
  -- Solve : 
          min -5.47e-05  max 4.81e-05
  -- Solve : 
          min -0.0162  max 0.0167
          min -0.0255  max 0.0225
          min -0.00815  max 0.000725
  -- Solve : 
          min -0.0711  max 50
Timestamp:		0.64sec / 5sec
  -- Solve : 
          min -6.56e-05  max 5.8e-05
  -- Solve : 
          min -0.0179  max 0.0183
          min -0.0284  max 0.0271
          min -0.0085  max 0.000804
  -- Solve : 
          min -0.0545  max 50
Timestamp:		0.68sec / 5sec
  -- Solve : 
          min -7.85e-05  max 6.97e-05
  -- Solve : 
          min -0.0205  max 0.0208
          min -0.0316  max 0.0324
          min -0.00885  max 0.000893
  -- Solve : 
          min -0.0501  max 50
Timestamp:		0.72sec / 5sec
  -- Solve : 
          min -9.57e-05  max 8.35e-05
  -- Solve : 
          min -0.0232  max 0.0244
          min -0.0351  max 0.0382
          min -0.00919  max 0.000986
  -- Solve : 
          min -0.05  max 50
Timestamp:		0.76sec / 5sec
  -- Solve : 
          min -0.000116  max 9.94e-05
  -- Solve : 
          min -0.026  max 0.0284
          min -0.0387  max 0.0444
          min -0.00951  max 0.0011
  -- Solve : 
          min -0.0564  max 50
Timestamp:		0.8sec / 5sec
  -- Solve : 
          min -0.00014  max 0.00012
  -- Solve : 
          min -0.0286  max 0.0324
          min -0.0435  max 0.0517
          min -0.00979  max 0.00128
  -- Solve : 
          min -0.0696  max 50
Timestamp:		0.84sec / 5sec
  -- Solve : 
          min -0.000167  max 0.000147
  -- Solve : 
          min -0.0317  max 0.0363
          min -0.0485  max 0.0598
          min -0.01  max 0.00149
  -- Solve : 
          min -0.0889  max 50
Timestamp:		0.88sec / 5sec
  -- Solve : 
          min -0.000196  max 0.000177
  -- Solve : 
          min -0.0353  max 0.04
          min -0.0531  max 0.0677
          min -0.0102  max 0.00172
  -- Solve : 
          min -0.107  max 50
Timestamp:		0.92sec / 5sec
  -- Solve : 
          min -0.000225  max 0.000211
  -- Solve : 
          min -0.0385  max 0.0432
          min -0.0569  max 0.0747
          min -0.0104  max 0.00199
  -- Solve : 
          min -0.139  max 50
Timestamp:		0.96sec / 5sec
  -- Solve : 
          min -0.000262  max 0.000245
  -- Solve : 
          min -0.0419  max 0.0459
          min -0.0596  max 0.0802
          min -0.0108  max 0.00224
  -- Solve : 
          min -0.222  max 50
Timestamp:		1sec / 5sec
  -- Solve : 
          min -0.000303  max 0.000279
  -- Solve : 
          min -0.0451  max 0.0482
          min -0.0614  max 0.0854
          min -0.0113  max 0.00262
  -- Solve : 
          min -0.299  max 50
Timestamp:		1.04sec / 5sec
  -- Solve : 
          min -0.000339  max 0.000311
  -- Solve : 
          min -0.0479  max 0.05
          min -0.0643  max 0.0928
          min -0.0117  max 0.00298
  -- Solve : 
          min -0.309  max 50
Timestamp:		1.08sec / 5sec
  -- Solve : 
          min -0.00037  max 0.000339
  -- Solve : 
          min -0.0503  max 0.0513
          min -0.07  max 0.0981
          min -0.012  max 0.00331
  -- Solve : 
          min -0.408  max 50
Timestamp:		1.12sec / 5sec
  -- Solve : 
          min -0.000408  max 0.000375
  -- Solve : 
          min -0.0523  max 0.0524
          min -0.0746  max 0.101
          min -0.0122  max 0.00365
  -- Solve : 
          min -0.483  max 50
Timestamp:		1.16sec / 5sec
  -- Solve : 
          min -0.000454  max 0.00043
  -- Solve : 
          min -0.054  max 0.0534
          min -0.0812  max 0.101
          min -0.0123  max 0.00404
  -- Solve : 
          min -0.562  max 50
Timestamp:		1.2sec / 5sec
  -- Solve : 
          min -0.000496  max 0.00048
  -- Solve : 
          min -0.0553  max 0.057
          min -0.087  max 0.107
          min -0.0127  max 0.00457
  -- Solve : 
          min -0.626  max 50
Timestamp:		1.24sec / 5sec
  -- Solve : 
          min -0.000548  max 0.000533
  -- Solve : 
          min -0.0563  max 0.0632
          min -0.0918  max 0.109
          min -0.013  max 0.00506
  -- Solve : 
          min -0.669  max 50
Timestamp:		1.28sec / 5sec
  -- Solve : 
          min -0.000611  max 0.000591
  -- Solve : 
          min -0.057  max 0.0684
          min -0.0958  max 0.107
          min -0.0134  max 0.00521
  -- Solve : 
          min -0.78  max 50
Timestamp:		1.32sec / 5sec
  -- Solve : 
          min -0.000661  max 0.000641
  -- Solve : 
          min -0.0584  max 0.0722
          min -0.0992  max 0.111
          min -0.0137  max 0.00555
  -- Solve : 
          min -0.717  max 50
Timestamp:		1.36sec / 5sec
  -- Solve : 
          min -0.000697  max 0.000681
  -- Solve : 
          min -0.0617  max 0.0767
          min -0.102  max 0.115
          min -0.014  max 0.00599
  -- Solve : 
          min -0.843  max 50
Timestamp:		1.4sec / 5sec
  -- Solve : 
          min -0.000741  max 0.000712
  -- Solve : 
          min -0.0666  max 0.0803
          min -0.104  max 0.118
          min -0.0142  max 0.00626
  -- Solve : 
          min -0.773  max 50
Timestamp:		1.44sec / 5sec
  -- Solve : 
          min -0.000782  max 0.000735
  -- Solve : 
          min -0.0712  max 0.0818
          min -0.105  max 0.12
          min -0.0144  max 0.00661
  -- Solve : 
          min -0.909  max 50
Timestamp:		1.48sec / 5sec
  -- Solve : 
          min -0.000811  max 0.000751
  -- Solve : 
          min -0.0754  max 0.0847
          min -0.104  max 0.123
          min -0.0145  max 0.00684
  -- Solve : 
          min -1.06  max 50
Timestamp:		1.52sec / 5sec
  -- Solve : 
          min -0.000861  max 0.000763
  -- Solve : 
          min -0.0792  max 0.0808
          min -0.103  max 0.126
          min -0.0147  max 0.00718
  -- Solve : 
          min -0.904  max 50
Timestamp:		1.56sec / 5sec
  -- Solve : 
          min -0.000901  max 0.000775
  -- Solve : 
          min -0.0825  max 0.0803
          min -0.102  max 0.129
          min -0.0154  max 0.00743
  -- Solve : 
          min -0.687  max 50
Timestamp:		1.6sec / 5sec
  -- Solve : 
          min -0.000932  max 0.000789
  -- Solve : 
          min -0.0855  max 0.083
          min -0.101  max 0.132
          min -0.0159  max 0.00777
  -- Solve : 
          min -0.548  max 50
Timestamp:		1.64sec / 5sec
  -- Solve : 
          min -0.000958  max 0.000801
  -- Solve : 
          min -0.088  max 0.086
          min -0.101  max 0.132
          min -0.0158  max 0.00814
  -- Solve : 
          min -0.461  max 50
Timestamp:		1.68sec / 5sec
  -- Solve : 
          min -0.001  max 0.000812
  -- Solve : 
          min -0.0898  max 0.0892
          min -0.103  max 0.132
          min -0.0157  max 0.00871
  -- Solve : 
          min -0.372  max 50
Timestamp:		1.72sec / 5sec
  -- Solve : 
          min -0.00105  max 0.00083
  -- Solve : 
          min -0.092  max 0.0917
          min -0.104  max 0.134
          min -0.0161  max 0.00945
  -- Solve : 
          min -0.418  max 50
Timestamp:		1.76sec / 5sec
  -- Solve : 
          min -0.00111  max 0.000856
  -- Solve : 
          min -0.0947  max 0.0954
          min -0.105  max 0.131
          min -0.0166  max 0.0102
  -- Solve : 
          min -0.424  max 50
Timestamp:		1.8sec / 5sec
  -- Solve : 
          min -0.00118  max 0.000881
  -- Solve : 
          min -0.0951  max 0.0962
          min -0.105  max 0.133
          min -0.0171  max 0.0111
  -- Solve : 
          min -0.367  max 50
Timestamp:		1.84sec / 5sec
  -- Solve : 
          min -0.00125  max 0.000906
  -- Solve : 
          min -0.0958  max 0.098
          min -0.104  max 0.143
          min -0.0179  max 0.0119
  -- Solve : 
          min -0.767  max 50
Timestamp:		1.88sec / 5sec
  -- Solve : 
          min -0.00131  max 0.000942
  -- Solve : 
          min -0.0958  max 0.0995
          min -0.104  max 0.153
          min -0.0183  max 0.0128
  -- Solve : 
          min -0.756  max 50
Timestamp:		1.92sec / 5sec
  -- Solve : 
          min -0.00138  max 0.000963
  -- Solve : 
          min -0.1  max 0.101
          min -0.104  max 0.159
          min -0.0187  max 0.0136
  -- Solve : 
          min -0.288  max 50
Timestamp:		1.96sec / 5sec
  -- Solve : 
          min -0.00144  max 0.00101
  -- Solve : 
          min -0.106  max 0.102
          min -0.104  max 0.159
          min -0.0189  max 0.0145
  -- Solve : 
          min -0.26  max 50
Timestamp:		2sec / 5sec
  -- Solve : 
          min -0.00148  max 0.00107
  -- Solve : 
          min -0.112  max 0.103
          min -0.104  max 0.154
          min -0.0193  max 0.0152
  -- Solve : 
          min -0.206  max 50
Timestamp:		2.04sec / 5sec
  -- Solve : 
          min -0.0015  max 0.00112
  -- Solve : 
          min -0.114  max 0.104
          min -0.104  max 0.149
          min -0.0193  max 0.0158
  -- Solve : 
          min -0.222  max 50
Timestamp:		2.08sec / 5sec
  -- Solve : 
          min -0.00152  max 0.00118
  -- Solve : 
          min -0.118  max 0.104
          min -0.107  max 0.143
          min -0.0193  max 0.0165
  -- Solve : 
          min -0.244  max 50
Timestamp:		2.12sec / 5sec
  -- Solve : 
          min -0.00153  max 0.00125
  -- Solve : 
          min -0.119  max 0.105
          min -0.117  max 0.143
          min -0.0192  max 0.0172
  -- Solve : 
          min -0.253  max 50
Timestamp:		2.16sec / 5sec
  -- Solve : 
          min -0.00152  max 0.00131
  -- Solve : 
          min -0.118  max 0.107
          min -0.127  max 0.149
          min -0.0194  max 0.0175
  -- Solve : 
          min -0.907  max 50
Timestamp:		2.2sec / 5sec
  -- Solve : 
          min -0.00148  max 0.00137
  -- Solve : 
          min -0.116  max 0.109
          min -0.135  max 0.156
          min -0.0202  max 0.0177
  -- Solve : 
          min -0.816  max 50
Timestamp:		2.24sec / 5sec
  -- Solve : 
          min -0.00144  max 0.00142
  -- Solve : 
          min -0.119  max 0.11
          min -0.143  max 0.16
          min -0.0209  max 0.0185
  -- Solve : 
          min -0.321  max 50
Timestamp:		2.28sec / 5sec
  -- Solve : 
          min -0.00139  max 0.00148
  -- Solve : 
          min -0.121  max 0.111
          min -0.148  max 0.161
          min -0.0209  max 0.0196
  -- Solve : 
          min -6.13e-35  max 50
Timestamp:		2.32sec / 5sec
  -- Solve : 
          min -0.00133  max 0.00155
  -- Solve : 
          min -0.122  max 0.112
          min -0.149  max 0.163
          min -0.0203  max 0.0205
  -- Solve : 
          min -6.06e-35  max 50
Timestamp:		2.36sec / 5sec
  -- Solve : 
          min -0.00135  max 0.00163
  -- Solve : 
          min -0.123  max 0.111
          min -0.146  max 0.161
          min -0.0194  max 0.0215
  -- Solve : 
          min -6.11e-35  max 50
Timestamp:		2.4sec / 5sec
  -- Solve : 
          min -0.0014  max 0.00169
  -- Solve : 
          min -0.121  max 0.11
          min -0.14  max 0.157
          min -0.0183  max 0.0219
  -- Solve : 
          min -6.24e-35  max 50
Timestamp:		2.44sec / 5sec
  -- Solve : 
          min -0.00145  max 0.00173
  -- Solve : 
          min -0.119  max 0.109
          min -0.132  max 0.152
          min -0.0173  max 0.0219
  -- Solve : 
          min -6.37e-35  max 50
Timestamp:		2.48sec / 5sec
  -- Solve : 
          min -0.00149  max 0.00176
  -- Solve : 
          min -0.114  max 0.113
          min -0.125  max 0.156
          min -0.0165  max 0.0216
  -- Solve : 
          min -6.48e-35  max 50
Timestamp:		2.52sec / 5sec
  -- Solve : 
          min -0.00151  max 0.00177
  -- Solve : 
          min -0.11  max 0.117
          min -0.127  max 0.159
          min -0.0172  max 0.0212
  -- Solve : 
          min -6.57e-35  max 50
Timestamp:		2.56sec / 5sec
  -- Solve : 
          min -0.00152  max 0.00176
  -- Solve : 
          min -0.112  max 0.119
          min -0.127  max 0.163
          min -0.0177  max 0.0205
  -- Solve : 
          min -6.64e-35  max 50
Timestamp:		2.6sec / 5sec
  -- Solve : 
          min -0.00152  max 0.00176
  -- Solve : 
          min -0.114  max 0.121
          min -0.125  max 0.164
          min -0.0176  max 0.0197
  -- Solve : 
          min -6.68e-35  max 50
Timestamp:		2.64sec / 5sec
  -- Solve : 
          min -0.00152  max 0.00175
  -- Solve : 
          min -0.116  max 0.123
          min -0.124  max 0.166
          min -0.0181  max 0.0193
  -- Solve : 
          min -6.7e-35  max 50
Timestamp:		2.68sec / 5sec
  -- Solve : 
          min -0.0015  max 0.00173
  -- Solve : 
          min -0.118  max 0.125
          min -0.119  max 0.163
          min -0.0186  max 0.0196
  -- Solve : 
          min -6.71e-35  max 50
Timestamp:		2.72sec / 5sec
  -- Solve : 
          min -0.00147  max 0.00172
  -- Solve : 
          min -0.12  max 0.125
          min -0.112  max 0.16
          min -0.0191  max 0.0199
  -- Solve : 
          min -6.69e-35  max 50
Timestamp:		2.76sec / 5sec
  -- Solve : 
          min -0.00147  max 0.0017
  -- Solve : 
          min -0.121  max 0.124
          min -0.102  max 0.155
          min -0.0195  max 0.0202
  -- Solve : 
          min -6.65e-35  max 50
Timestamp:		2.8sec / 5sec
  -- Solve : 
          min -0.0015  max 0.00167
  -- Solve : 
          min -0.121  max 0.121
          min -0.0984  max 0.149
          min -0.0197  max 0.0205
  -- Solve : 
          min -6.6e-35  max 50
Timestamp:		2.84sec / 5sec
  -- Solve : 
          min -0.0015  max 0.00164
  -- Solve : 
          min -0.12  max 0.118
          min -0.0936  max 0.157
          min -0.02  max 0.0206
  -- Solve : 
          min -6.54e-35  max 50
Timestamp:		2.88sec / 5sec
  -- Solve : 
          min -0.00149  max 0.00161
  -- Solve : 
          min -0.119  max 0.115
          min -0.0871  max 0.162
          min -0.0203  max 0.0207
  -- Solve : 
          min -6.46e-35  max 50
Timestamp:		2.92sec / 5sec
  -- Solve : 
          min -0.00147  max 0.00156
  -- Solve : 
          min -0.117  max 0.112
          min -0.0887  max 0.164
          min -0.0205  max 0.0206
  -- Solve : 
          min -6.36e-35  max 50
Timestamp:		2.96sec / 5sec
  -- Solve : 
          min -0.00143  max 0.00152
  -- Solve : 
          min -0.115  max 0.111
          min -0.0927  max 0.162
          min -0.0207  max 0.0207
  -- Solve : 
          min -6.26e-35  max 50
Timestamp:		3sec / 5sec
  -- Solve : 
          min -0.00138  max 0.00146
  -- Solve : 
          min -0.114  max 0.11
          min -0.0986  max 0.157
          min -0.021  max 0.0216
  -- Solve : 
          min -6.16e-35  max 50
Timestamp:		3.04sec / 5sec
  -- Solve : 
          min -0.00143  max 0.00141
  -- Solve : 
          min -0.112  max 0.108
          min -0.104  max 0.152
          min -0.0212  max 0.0227
  -- Solve : 
          min -6.07e-35  max 50
Timestamp:		3.08sec / 5sec
  -- Solve : 
          min -0.00149  max 0.00135
  -- Solve : 
          min -0.11  max 0.109
          min -0.108  max 0.148
          min -0.0216  max 0.0235
  -- Solve : 
          min -5.99e-35  max 50
Timestamp:		3.12sec / 5sec
  -- Solve : 
          min -0.00156  max 0.00129
  -- Solve : 
          min -0.106  max 0.107
          min -0.112  max 0.144
          min -0.0222  max 0.0238
  -- Solve : 
          min -5.94e-35  max 50
Timestamp:		3.16sec / 5sec
  -- Solve : 
          min -0.0016  max 0.00123
  -- Solve : 
          min -0.103  max 0.105
          min -0.114  max 0.14
          min -0.0226  max 0.0237
  -- Solve : 
          min -5.9e-35  max 50
Timestamp:		3.2sec / 5sec
  -- Solve : 
          min -0.00163  max 0.00117
  -- Solve : 
          min -0.102  max 0.103
          min -0.115  max 0.137
          min -0.0231  max 0.0234
  -- Solve : 
          min -5.87e-35  max 50
Timestamp:		3.24sec / 5sec
  -- Solve : 
          min -0.00165  max 0.00111
  -- Solve : 
          min -0.103  max 0.109
          min -0.115  max 0.134
          min -0.0234  max 0.0232
  -- Solve : 
          min -5.87e-35  max 50
Timestamp:		3.28sec / 5sec
  -- Solve : 
          min -0.00166  max 0.00105
  -- Solve : 
          min -0.105  max 0.117
          min -0.113  max 0.135
          min -0.0236  max 0.023
  -- Solve : 
          min -5.87e-35  max 50
Timestamp:		3.32sec / 5sec
  -- Solve : 
          min -0.00168  max 0.000987
  -- Solve : 
          min -0.106  max 0.119
          min -0.109  max 0.137
          min -0.0238  max 0.0229
  -- Solve : 
          min -5.87e-35  max 50
Timestamp:		3.36sec / 5sec
  -- Solve : 
          min -0.00169  max 0.00102
  -- Solve : 
          min -0.111  max 0.119
          min -0.111  max 0.137
          min -0.0238  max 0.0229
  -- Solve : 
          min -5.88e-35  max 50
Timestamp:		3.4sec / 5sec
  -- Solve : 
          min -0.00169  max 0.00107
  -- Solve : 
          min -0.109  max 0.119
          min -0.113  max 0.138
          min -0.0239  max 0.0229
  -- Solve : 
          min -5.89e-35  max 50
Timestamp:		3.44sec / 5sec
  -- Solve : 
          min -0.0017  max 0.0011
  -- Solve : 
          min -0.108  max 0.119
          min -0.114  max 0.137
          min -0.0237  max 0.0229
  -- Solve : 
          min -5.89e-35  max 50
Timestamp:		3.48sec / 5sec
  -- Solve : 
          min -0.0017  max 0.00114
  -- Solve : 
          min -0.107  max 0.119
          min -0.115  max 0.135
          min -0.0235  max 0.0229
  -- Solve : 
          min -5.9e-35  max 50
Timestamp:		3.52sec / 5sec
  -- Solve : 
          min -0.00171  max 0.00118
  -- Solve : 
          min -0.107  max 0.119
          min -0.113  max 0.134
          min -0.0232  max 0.0229
  -- Solve : 
          min -5.91e-35  max 50
Timestamp:		3.56sec / 5sec
  -- Solve : 
          min -0.00171  max 0.00123
  -- Solve : 
          min -0.109  max 0.12
          min -0.111  max 0.134
          min -0.023  max 0.0229
  -- Solve : 
          min -5.91e-35  max 50
Timestamp:		3.6sec / 5sec
  -- Solve : 
          min -0.00172  max 0.00127
  -- Solve : 
          min -0.11  max 0.119
          min -0.11  max 0.136
          min -0.0226  max 0.0229
  -- Solve : 
          min -5.93e-35  max 50
Timestamp:		3.64sec / 5sec
  -- Solve : 
          min -0.00174  max 0.00129
  -- Solve : 
          min -0.113  max 0.118
          min -0.11  max 0.139
          min -0.0221  max 0.0228
  -- Solve : 
          min -5.94e-35  max 50
Timestamp:		3.68sec / 5sec
  -- Solve : 
          min -0.00177  max 0.00134
  -- Solve : 
          min -0.115  max 0.118
          min -0.11  max 0.143
          min -0.0216  max 0.0231
  -- Solve : 
          min -5.96e-35  max 50
Timestamp:		3.72sec / 5sec
  -- Solve : 
          min -0.00179  max 0.00138
  -- Solve : 
          min -0.116  max 0.117
          min -0.113  max 0.147
          min -0.0211  max 0.0236
  -- Solve : 
          min -5.99e-35  max 50
Timestamp:		3.76sec / 5sec
  -- Solve : 
          min -0.0018  max 0.00142
  -- Solve : 
          min -0.117  max 0.118
          min -0.117  max 0.151
          min -0.021  max 0.024
  -- Solve : 
          min -6.01e-35  max 50
Timestamp:		3.8sec / 5sec
  -- Solve : 
          min -0.0018  max 0.00145
  -- Solve : 
          min -0.123  max 0.119
          min -0.123  max 0.153
          min -0.0215  max 0.0244
  -- Solve : 
          min -6.04e-35  max 50
Timestamp:		3.84sec / 5sec
  -- Solve : 
          min -0.00179  max 0.00148
  -- Solve : 
          min -0.129  max 0.119
          min -0.128  max 0.153
          min -0.0218  max 0.0247
  -- Solve : 
          min -6.06e-35  max 50
Timestamp:		3.88sec / 5sec
  -- Solve : 
          min -0.00178  max 0.00151
  -- Solve : 
          min -0.131  max 0.119
          min -0.133  max 0.151
          min -0.022  max 0.0248
  -- Solve : 
          min -6.07e-35  max 50
Timestamp:		3.92sec / 5sec
  -- Solve : 
          min -0.00177  max 0.00153
  -- Solve : 
          min -0.132  max 0.121
          min -0.133  max 0.146
          min -0.0221  max 0.0249
  -- Solve : 
          min -6.05e-35  max 50
Timestamp:		3.96sec / 5sec
  -- Solve : 
          min -0.00174  max 0.00156
  -- Solve : 
          min -0.132  max 0.123
          min -0.133  max 0.149
          min -0.0221  max 0.0248
  -- Solve : 
          min -6e-35  max 50
Timestamp:		4sec / 5sec
  -- Solve : 
          min -0.00171  max 0.00158
  -- Solve : 
          min -0.13  max 0.123
          min -0.131  max 0.152
          min -0.0221  max 0.025
  -- Solve : 
          min -5.91e-35  max 50
Timestamp:		4.04sec / 5sec
  -- Solve : 
          min -0.00168  max 0.00161
  -- Solve : 
          min -0.129  max 0.123
          min -0.128  max 0.151
          min -0.0219  max 0.0263
  -- Solve : 
          min -5.82e-35  max 50
Timestamp:		4.08sec / 5sec
  -- Solve : 
          min -0.00164  max 0.00163
  -- Solve : 
          min -0.127  max 0.124
          min -0.124  max 0.151
          min -0.0217  max 0.0275
  -- Solve : 
          min -5.76e-35  max 50
Timestamp:		4.12sec / 5sec
  -- Solve : 
          min -0.0016  max 0.00166
  -- Solve : 
          min -0.126  max 0.126
          min -0.126  max 0.152
          min -0.0214  max 0.0284
  -- Solve : 
          min -5.76e-35  max 50
Timestamp:		4.16sec / 5sec
  -- Solve : 
          min -0.00155  max 0.00168
  -- Solve : 
          min -0.124  max 0.129
          min -0.129  max 0.162
          min -0.0214  max 0.0289
  -- Solve : 
          min -5.76e-35  max 50
Timestamp:		4.2sec / 5sec
  -- Solve : 
          min -0.00151  max 0.0017
  -- Solve : 
          min -0.123  max 0.132
          min -0.133  max 0.168
          min -0.0215  max 0.029
  -- Solve : 
          min -5.75e-35  max 50
Timestamp:		4.24sec / 5sec
  -- Solve : 
          min -0.00147  max 0.00172
  -- Solve : 
          min -0.122  max 0.135
          min -0.135  max 0.173
          min -0.0213  max 0.0285
  -- Solve : 
          min -5.75e-35  max 50
Timestamp:		4.28sec / 5sec
  -- Solve : 
          min -0.00143  max 0.00174
  -- Solve : 
          min -0.124  max 0.135
          min -0.135  max 0.173
          min -0.0212  max 0.0275
  -- Solve : 
          min -5.75e-35  max 50
Timestamp:		4.32sec / 5sec
  -- Solve : 
          min -0.00139  max 0.00176
  -- Solve : 
          min -0.124  max 0.132
          min -0.132  max 0.173
          min -0.0213  max 0.0266
  -- Solve : 
          min -5.84e-35  max 50
Timestamp:		4.36sec / 5sec
  -- Solve : 
          min -0.00136  max 0.00178
  -- Solve : 
          min -0.124  max 0.128
          min -0.128  max 0.168
          min -0.0215  max 0.0276
  -- Solve : 
          min -5.94e-35  max 50
Timestamp:		4.4sec / 5sec
  -- Solve : 
          min -0.00133  max 0.0018
  -- Solve : 
          min -0.123  max 0.126
          min -0.125  max 0.163
          min -0.0216  max 0.0285
  -- Solve : 
          min -6.03e-35  max 50
Timestamp:		4.44sec / 5sec
  -- Solve : 
          min -0.00131  max 0.0018
  -- Solve : 
          min -0.124  max 0.127
          min -0.121  max 0.167
          min -0.0217  max 0.0293
  -- Solve : 
          min -6.1e-35  max 50
Timestamp:		4.48sec / 5sec
  -- Solve : 
          min -0.00128  max 0.0018
  -- Solve : 
          min -0.125  max 0.129
          min -0.116  max 0.173
          min -0.0217  max 0.0301
  -- Solve : 
          min -6.14e-35  max 50
Timestamp:		4.52sec / 5sec
  -- Solve : 
          min -0.00126  max 0.00179
  -- Solve : 
          min -0.125  max 0.132
          min -0.117  max 0.176
          min -0.022  max 0.0312
  -- Solve : 
          min -6.16e-35  max 50
Timestamp:		4.56sec / 5sec
  -- Solve : 
          min -0.00124  max 0.00178
  -- Solve : 
          min -0.124  max 0.134
          min -0.119  max 0.176
          min -0.0222  max 0.0317
  -- Solve : 
          min -6.16e-35  max 50
Timestamp:		4.6sec / 5sec
  -- Solve : 
          min -0.00122  max 0.00175
  -- Solve : 
          min -0.122  max 0.134
          min -0.123  max 0.174
          min -0.0225  max 0.032
  -- Solve : 
          min -6.15e-35  max 50
Timestamp:		4.64sec / 5sec
  -- Solve : 
          min -0.00121  max 0.00171
  -- Solve : 
          min -0.12  max 0.133
          min -0.125  max 0.171
          min -0.0228  max 0.032
  -- Solve : 
          min -6.12e-35  max 50
Timestamp:		4.68sec / 5sec
  -- Solve : 
          min -0.0012  max 0.00167
  -- Solve : 
          min -0.118  max 0.131
          min -0.131  max 0.168
          min -0.023  max 0.0318
  -- Solve : 
          min -6.08e-35  max 50
Timestamp:		4.72sec / 5sec
  -- Solve : 
          min -0.00121  max 0.00163
  -- Solve : 
          min -0.116  max 0.128
          min -0.136  max 0.163
          min -0.0233  max 0.0315
  -- Solve : 
          min -6.04e-35  max 50
Timestamp:		4.76sec / 5sec
  -- Solve : 
          min -0.00122  max 0.00158
  -- Solve : 
          min -0.114  max 0.126
          min -0.141  max 0.158
          min -0.0238  max 0.031
  -- Solve : 
          min -6e-35  max 50
Timestamp:		4.8sec / 5sec
  -- Solve : 
          min -0.00123  max 0.00154
  -- Solve : 
          min -0.113  max 0.124
          min -0.143  max 0.153
          min -0.0242  max 0.0304
  -- Solve : 
          min -5.96e-35  max 50
Timestamp:		4.84sec / 5sec
  -- Solve : 
          min -0.00124  max 0.00149
  -- Solve : 
          min -0.111  max 0.121
          min -0.142  max 0.148
          min -0.0246  max 0.0298
  -- Solve : 
          min -5.93e-35  max 50
Timestamp:		4.88sec / 5sec
  -- Solve : 
          min -0.00124  max 0.00144
  -- Solve : 
          min -0.109  max 0.118
          min -0.139  max 0.145
          min -0.025  max 0.0292
  -- Solve : 
          min -5.9e-35  max 50
Timestamp:		4.92sec / 5sec
  -- Solve : 
          min -0.00124  max 0.00139
  -- Solve : 
          min -0.107  max 0.116
          min -0.135  max 0.148
          min -0.0253  max 0.0287
  -- Solve : 
          min -5.88e-35  max 50
Timestamp:		4.96sec / 5sec
  -- Solve : 
          min -0.00123  max 0.00133

Heat transfer:		-55.4W/m
Heat transfer coef:	3.69W/m^2K
Prandtl Number:		0.713
Beta:			0.003361/K
Thermal diffusivity:	2.22e-05m^2/s

NbBoundaryElements:	210
NbTriangles:		3170
NbVertices:		1691
nDoF (T & Psi):		1691
nDoF (u1,u2):		6551

  number of required edges : 0

convective_rolls:
  Normal end of execution.
  current line = 219
exit(0)
 err code 0 ,  mpirank 0
 CodeAlloc : nb ptr  4450,  size :511520 mpirank: 0
Ok: Normal End