# Title: Flow through a divergent channel
#
# Description:
#
# A test case initially presented by Almgren et al \cite{almgren97}.
# The Euler equations are solved in a divergent channel for a unit
# inflow velocity on the left boundary and outflow on the right
# boundary.
#
# Tables \ref{channel-x} and \ref{channel-y} illustrate the errors and
# convergence orders obtained for both components of the velocity when
# the resolution varies. Richardson extrapolation is used.  The errors
# are computed either on the whole domain (All cells) or on the cells
# whose parents at level 5 are entirely contained in the fluid (Full
# 128 cells).
#
# Close to second-order convergence is obtained in the bulk of the
# fluid, reducing to first-order close to the boundaries. The errors
# are small in all cases (with a maximum of .5\%) and comparable to
# that obtained by Almgren et al using a different discretisation.
#
# \input{convergence.tex}
#
# Author: St\'ephane Popinet
# Command: sh channel.sh channel.gfs
# Version: 1.1.0
# Required files: channel.sh orderU.ref orderfU.ref orderV.ref orderfV.ref
# Running time: 3 minutes
# Generated files: convergence.tex
#
4 3 GfsSimulation GfsBox GfsGEdge {} {
    Time { end = 1 }
    AdvectionParams { cfl = 0.9 }
    ProjectionParams { tolerance = 1e-6 }
    ApproxProjectionParams { tolerance = 1e-6 }
    Refine LEVEL
    Global {
        double channel (double x) {
            double y1 = 0.2/4.;
            double y2 = 1e-6/4.;
            
            return x <= -0.25 ? y1 : 
                   x < 0.25 ? y2 + 0.5*(y1 - y2)*(1. + cos (2.*M_PI*(x + 0.25))) : 
                   y2;
        }
    }
    Solid (0.125 - channel (x) - y) { scale = 4 tx = 1.5 }
    Solid (y + 0.125 - channel (x)) { scale = 4 tx = 1.5 }
    Init {} { U = 1 }
    OutputSimulation { start = end } sim-LEVEL {
        variables = U,V,P
    }
}
GfsBox { left = Boundary { BcDirichlet U 1 } }
GfsBox {}
GfsBox {}
GfsBox { right = BoundaryOutflow }
1 2 right
2 3 right
3 4 right