  We consider the numerical solution of an acoustic scattering problem by the
Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded
domain in $\mathbb{R}^2$. In order to apply the PWDG method, we introduce an
artificial boundary to truncate the domain, and we impose a non-local
Dirichlet-to-Neumann (DtN) boundary conditions on the artificial curve. To
define the method, we introduce new consistent numerical fluxes that
incorporate the truncated series of the DtN map. Error estimates with respect
to the truncation order of the DtN map, and with respect to mesh width are
derived. Numerical results suggest that the accuracy of the PWDG method for the
acoustic scattering problem can be significantly improved by using DtN boundary
conditions.
