GfsSpatialSum

From Gerris

GfsSpatialSum defines a new GfsConstant containing the spatial sum (spatial integral) of a GfsFunction.

The syntax in parameter files is

[ GfsConstant ] [ GfsFunction ] 

For example, the following computes the spatial sum of Variable U at every time step, placing the result in a Constant Ubar

 SpatialSum { istep = 1 } Ubar U

Examples

• Forced isotropic turbulence in a triply-periodic box

  SpatialSum { istep = 1 } SU U

  SpatialSum { istep = 1 } SV V

  SpatialSum { istep = 1 } SW W

  SpatialSum { istep = 1 } Un Velocity

  SpatialSum { istep = 1 } Dissipation { 
      return MU*(dx("U")*dx("U") + dy("U")*dy("U") + dz("U")*dz("U") + 
                 dx("V")*dx("V") + dy("V")*dy("V") + dz("V")*dz("V") +
                 dx("W")*dx("W") + dy("W")*dy("W") + dz("W")*dz("W"));
  } 

  SpatialSum { istep = 1 } FluctKinEn {
      return 0.5*((U - Ubar)*(U - Ubar) + 
                  (V - Vbar)*(V - Vbar) +
                  (W - Wbar)*(W - Wbar));
  }