@TechReport{	  it:2013-013,
  author	= {Jens Berg and Jan Nordstr{\"o}m},
  title		= {Duality Based Boundary Conditions and Dual Consistent
		  Finite Difference Discretizations of the {N}avier-{S}tokes
		  and {E}uler Equations},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2013},
  number	= {2013-013},
  month		= may,
  abstract	= {In this paper we derive new farfield boundary conditions
		  for the time-dependent Navier-Stokes and Euler equations in
		  two space dimensions. The new boundary conditions are
		  derived by simultaneously considering well-posedess of both
		  the primal and dual problems. We moreover require that the
		  boundary conditions for the primal and dual Navier-Stokes
		  equations converge to well-posed boundary conditions for
		  the primal and dual Euler equations.
		  
		  We perform computations with a high-order finite difference
		  scheme on summation-by-parts form with the new boundary
		  conditions imposed weakly by the simultaneous approximation
		  term. We prove that the scheme is both energy stable and
		  dual consistent and show numerically that both linear and
		  non-linear integral functionals become superconvergent.}
}