# Title: Poiseuille flow
#
# Description:
#
# A simple parabolic Poiseuille flow in a periodic channel with a
# constant along-channel acceleration $a$. The theoretical solution is given by:
# $$u(y)={a\over 2\nu}(1/4-y^2)$$
# Figure \ref{convergence} illustrates the maximum error between the
# computed and theoretical solutions as a function of spatial
# resolution.
#
# \begin{figure}[htbp]
# \caption{\label{convergence}Convergence of the maximum error as a function
# of resolution (number of grid points across the channel).}
# \begin{center}
# \includegraphics[width=\hsize]{convergence.eps}
# \end{center}
# \end{figure}
#
# Author: St\'ephane Popinet
# Command: sh poiseuille.sh
# Version: 1.2.0
# Required files: poiseuille.sh error.ref
# Generated files: convergence.eps
#
1 1 GfsSimulation GfsBox GfsGEdge {} {
    Refine LEVEL
    # use backward Euler to avoid Crank-Nicholson oscillations in time
    SourceViscosity 1. { beta = 1 }
    Source U 1

    # we need this so that acceleration can be balanced by viscous stress
    # and yes, fixme, this is a mess...
    AdvectionParams { gc = 1 }

    EventStop { istep = 1 } U 1e-6 DU
    ProjectionParams { tolerance = 1e-6 }
    ApproxProjectionParams { tolerance = 1e-6 }
    OutputErrorNorm { start = end } { awk '{print LEVEL,$5,$7,$9}' } { v = U } { 
        s = 1./2.*(1./4 - y*y) 
    }
}
GfsBox {
    bottom = Boundary {
        BcDirichlet U 0 
        BcDirichlet V 0 
    }
    top = Boundary {
        BcDirichlet U 0 
        BcDirichlet V 0 
    }
}
1 1 right