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 following formatting:

Description time: 1.2 first: 1e-2 second: 3e-2 infty: 6e-3 bias: 1e-6

where Description is a description of the scalar field.

The syntax in parameter files is:

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

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.

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 
    }

• 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
  }