///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
/// 
/// =========================================================================
//! @examplefile inertia_upw.icc The inertia term of the Navier-Stokes equation with the discontinuous Galerkin method -- upwinding variant
#include "sgn.icc"
form inertia_upw (field w, trial u, test v, 
  integrate_option iopt = integrate_option())
{
  return integrate ("internal_sides",
     0.5*abs(dot(average(w),normal()))*dot(jump(u),jump(v)));
}
form d_inertia_upw (field w, trial dw, field u, test v, 
  integrate_option iopt = integrate_option())
{
  return integrate ("internal_sides",
     0.5*compose (sgn, dot(average(w),normal()))
         *dot(average(dw),normal())*dot(jump(u),jump(v)));
}