# Title: Hydrostatic balance with quadratic pressure profile
#
# Description:
#
# Same test as before but for a quadratic pressure profile.
#
# Author: St\'ephane Popinet
# Command: gerris2D quadratic.gfs
# Version: 1.2.0
# Required files: quadratic.gfs
1 0 GfsSimulation GfsBox GfsGEdge {} {
    Refine 3

    # This test case only works for constant refinement
    #    Refine (x*x + y*y < 0.2*0.2 ? 4 : 3) 

    # Note: it is important to use 'cy' rather than 'y' in the formula
    # below so that the hydrostatic density distribution is correct
    # even for 'cut cells'
    Init {} { rho = (cy + 0.5) }

    Source V -rho
    SourceViscosity 1e-2
    Solid (ellipse(0.,0.,0.24,0.24))
    Time { iend = 10 }
    ApproxProjectionParams { tolerance = 1e-12 }
    ProjectionParams { tolerance = 1e-12 }

    OutputScalarNorm { istep = 1 } v { v = V }
    # Checks that the pressure profile is close to the exact solution
    OutputErrorNorm { istep = 1 } p { v = P } {
        s = -(cy*cy/2. + 0.5*cy) 
        unbiased = 1 
    }
    EventScript { start = end } { 
        if awk '{if ($9 > 1e-12) exit (1);}' < v ; then :
        else
            exit $GFS_STOP;
        fi        
        if awk '{if ($9 > 1e-12) exit (1);}' < p ; then :
        else
            exit $GFS_STOP;
        fi
    } 
}
GfsBox {}