Strong compact formalism for characteristic boundary conditions with discontinuous spectral methods

Abstract

Characteristic boundary conditions for the Navier-Stokes equations (NSCBC) are implemented for the first time with discontinuous spectral methods, namely the spectral difference and flux reconstruction. The implementation makes use of the resolution by these methods of the strong form of the Navier-Stokes equations by applying these conditions through a flux balance regularization which takes the form of a generalized element-compact correction polynomial. It is shown to be at least as effective as similar implementations in finite volume solvers, and sustains arbitrarily-high orders of accuracy on hexahedral-based unstructured meshes. Further, Navier-Stokes time-domain impedance boundary conditions are derived and implemented as a NSCBC sub-class. They account for the diffusive process at the wall and are shown to properly resolve the broadband response of porous materials under normal and grazing flow conditions. The ability of these NSCBC in preventing the appearance of spurious reflections at the boundaries is demonstrated through a varied series of bench-marking simulations. They effectively shield the inner computational domain from any far-field unphysical contamination. Overall, this work enables the use of strong discontinuous spectral methods to study unsteady problems on complex geometries.