The present study is aimed at applying a recently developed generalized equation of state algorithm along with the system of equations for a time dependent outflow boundary that not only allows more general fluids to be computed, but also uses theoretical results on well-posedness of Navier-Stokes boundary conditions to construct a systematic method for specifying these boundary conditions. An exact "discretely" non-reflecting boundary condition is derived for the three-dimensional filtered compressible Navier-Stokes equations based on Cartesian coordinates which are discretized with finite volume schemes. The test results and comparisons with other methods were conducted to explore its precision and robustness. The analysis extends the work by Poinsot, T. J. and Lele, S. K. (1992) to a three-dimensional pipe geometry, and the work by Xu, X. (2002) to the developing flows of general fluids.