GfsOutputErrorNorm

From Gerris

GfsOutputErrorNorm is used to write the norms of the difference between a scalar field and a user-defined reference field.

The norms are written using the same formatting as for GfsOutputScalarNorm.

The syntax in parameter files is:

[ GfsOutputScalar ] {
  s = [ GfsFunction ]
  unbiased = 1
  v = Error
  w = [ GfsFunction ]
  relative = 0
}

where s is the function defining the reference field and v is used to store the difference between the scalar and reference fields (v can be left undefined in which case a temporary variable is used).

If unbiased is set to one (default is zero), the bias (i.e. mean value of the difference) is substracted before computing the norms.

The norms can be weighted using the optional parameter w.

If relative is set to one, the norms are divided by the corresponding norms of the reference solution.

Examples

• Convergence of the Poisson solver

  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

  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 Godunov advection scheme

  OutputErrorNorm { start = end } { awk '{ print LEVEL " " $5 " " $7 " " $9}' } { v = T } {
    s = {
      double r2 = x*x + y*y; 
      double coeff = 20. + 20000.*r2*r2*r2*r2;
      return (1. + cos(20.*x)*cos(20.*y))*exp(-coeff*r2)/2.;
    }
  }

• Time-reversed VOF advection in a shear flow

    OutputErrorNorm { start = end } norms { v = T } {
        s = Tref v = DT
    }

• Time-reversed advection with curvature-based refinement

    OutputErrorNorm { start = end } norms { v = T } {
        s = Tref v = DT
    }

• Convergence for a simple periodic problem

  OutputErrorNorm { start = end } stdout { v = U } {
    s = (1. - 2.*cos (2.*M_PI*(x - t))*sin (2.*M_PI*(y - t)))
  }

• Potential flow around a sphere

    OutputErrorNorm { start = end } { awk '{ print LEVEL " " $7 " " $9}' } { v = U } {
 	s = (dx("Phi") + 1.)
    }

• Poiseuille flow

    OutputErrorNorm { start = end } { awk '{print LEVEL,$5,$7,$9}' } { v = U } { 
        s = 1./2.*(1./4 - y*y) 
    }

• Hydrostatic balance with quadratic pressure profile

    OutputErrorNorm { istep = 1 } p { v = P } {
        s = -(cy*cy/2. + 0.5*cy) 
        unbiased = 1 
    }

• Translation of an hexagon in a uniform flow

  OutputErrorNorm { istep = 1 } {
      awk '{ printf ("%e %e %e %e\n", $3, $5, $7, $9) }' > momentumerror-ORDER
  } { v = sqrt((U - 1.)*(U - 1.) + V*V) } { s = 0. }

• Geostrophic adjustment

  OutputErrorNorm { istep = 1 } { awk '{print $3/1.0285e-4/3600./24. " " $9*1000e6*1.0285e-4*1.0285e-4/0.01;}' > e } { v = P } {
    s = (5.667583815e-4*exp (-100.*(x*x + y*y)))
    unbiased = 1
    v = E
  }

• Oscillations in a parabolic container

    OutputErrorNorm { istep = 1 } error-LEVEL { v = P } {
	s = Pt
	v = DP
    }

• Advection of a cosine bell around the sphere

  OutputErrorNorm { istep = 1 } { awk '{ print LEVEL,$3,$5,$7,$9}' > error-LEVEL-ALPHA } { v = T } {
      s = bell(x,y,t)
      v = E
      relative = 1
  }