GfsPoisson

From Gerris

Examples

• Convergence of the Poisson solver

1 0 GfsPoisson GfsBox GfsGEdge {} {
  Time { iend = 10 }
  Refine LEVEL
  ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 }
  Init {} {
    Div = {
      int k = 3, l = 3;
      return -M_PI*M_PI*(k*k + l*l)*sin (M_PI*k*x)*sin (M_PI*l*y);
    }
  }
  OutputTime { istep = 1 } {
    awk '{print n++, $8}' > time
  }
  OutputProjectionStats { istep = 1 } {
    awk '{
      if ($1 == "niter:") printf ("%d ", $2);
      if ($1 == "residual.infty:") print $3 " " $4;
    }' > proj
  }
  OutputErrorNorm { start = end } {
    awk '{print LEVEL " " $5 " " $7 " " $9}' >> error 
  } { v = P } {
    s = (sin (M_PI*3.*x)*sin (M_PI*3.*y))
    unbiased = 1
  }
}

• Convergence with a refined circle

1 0 GfsPoisson GfsBox GfsGEdge {} {
  Time { iend = 10 }
  Refine (x*x + y*y <= 0.25*0.25 ? LEVEL + 2 : LEVEL)
  ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 }
  Init {} {
    Div = {
      int k = 3, l = 3;
      return -M_PI*M_PI*(k*k + l*l)*sin (M_PI*k*x)*sin (M_PI*l*y);
    }
  }
  OutputTime { istep = 1 } {
      awk '{print n++, $8}' > time
  }
  OutputProjectionStats { istep = 1 } {
    awk '{
      if ($1 == "niter:") printf ("%d ", $2);
      if ($1 == "residual.infty:") print $3 " " $4;
    }' > proj
  }
  OutputErrorNorm { start = end } {
    awk '{print LEVEL " " $5 " " $7 " " $9}' >> error 
  } { v = P } {
    s = (sin (M_PI*3.*x)*sin (M_PI*3.*y))
    unbiased = 1
  }
}

• Convergence of the Poisson solver with solid boundaries

1 0 GfsPoisson GfsBox GfsGEdge {} {
  Time { iend = 10 }
  Refine LEVEL
  Solid (ellipse (0, 0, 0.25, 0.25))
  ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 erelax = 2 }
  Init {} {
    Div = {
      int k = 3, l = 3;
      return -M_PI*M_PI*(k*k + l*l)*sin (M_PI*k*x)*sin (M_PI*l*y);
    }
  }
  OutputTime { istep = 1 } {
    awk '{print n++, $8}' > time
  }
  OutputProjectionStats { istep = 1 } {
    awk '{
      if ($1 == "niter:") printf ("%d ", $2);
      if ($1 == "residual.infty:") print $3 " " $4;
    }' > proj
  }
  OutputSimulation { start = end } sim-LEVEL { variables = P }
}

• Star-shaped solid boundary with refinement

1 0 GfsPoisson GfsBox GfsGEdge {} {
    Time { iend = 10 }
    Refine LEVEL
    RefineSolid (LEVEL + 2)
    Solid ({
            double dr = 0.1;
            double theta = atan2 (y, x);
            double radius = 0.79*(0.45 - dr + dr*cos (6.*theta));
            return x*x + y*y - radius*radius;
          })
    ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 }
    Init {} {
        Div = {
            int k = 3, l = 3;
            return -M_PI*M_PI*(k*k + l*l)*sin (M_PI*k*x)*sin (M_PI*l*y);
        }
    }
    OutputTime { istep = 1 } {
        awk '{print n++, $8}' > time
    }
    OutputProjectionStats { istep = 1 } {
        awk '{
      if ($1 == "niter:") printf ("%d ", $2);
      if ($1 == "residual.infty:") print $3 " " $4;
    }' > proj
    }
    OutputSimulation { start = end } sim-LEVEL { variables = P }
}

• Star-shaped solid boundary

1 0 GfsPoisson GfsBox GfsGEdge {} {
    Time { iend = 10 }
    Refine LEVEL
    Solid ({
            double dr = 0.1;
            double theta = atan2 (y, x);
            double radius = 0.79*(0.45 - dr + dr*cos (6.*theta));
            return x*x + y*y - radius*radius;
          })
    ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 erelax = 2 }
    Init {} {
        Div = {
            int k = 3, l = 3;
            return -M_PI*M_PI*(k*k + l*l)*sin (M_PI*k*x)*sin (M_PI*l*y);
        }
    }
    OutputTime { istep = 1 } {
        awk '{print n++, $8}' > time
    }
    OutputProjectionStats { istep = 1 } {
        awk '{
      if ($1 == "niter:") printf ("%d ", $2);
      if ($1 == "residual.infty:") print $3 " " $4;
    }' > proj
    }
    OutputSimulation { start = end } sim-LEVEL { variables = P }
}

• Thin wall at box boundary

4 3 GfsPoisson GfsBox GfsGEdge {} {
  Time { iend = 10 }
  Refine LEVEL
  ApproxProjectionParams { nrelax = 4 tolerance = 1e-30 erelax = 2 }
  Init {} {
    Div = {
      int k = 3, l = 3;
      x = (x - 0.5)/2.;
      y = (y + 0.5)/2.;
      return -M_PI*M_PI*(k*k + l*l)*sin (M_PI*k*x)*sin (M_PI*l*y);
    }
  }
  OutputTime { istep = 1 } {
    awk '{print n++, $8}' > time
  }
  OutputProjectionStats { istep = 1 } {
    awk '{
      if ($1 == "niter:") printf ("%d ", $2);
      if ($1 == "residual.infty:") print $3 " " $4;
    }' > proj
  }
  OutputSimulation { start = end } sim-LEVEL { variables = P }
}

• Poisson solution in a dumbbell-shaped domain

1 0 GfsPoisson GfsBox GfsGEdge {} {
  Refine 3
  ApproxProjectionParams { nitermax = 1000 minlevel = 1 tolerance = 1e-30 }
  Solid dumbell.gts
  Init {} { Div = y }
  OutputProjectionStats { istep = 1 } stdout
}