A p-adaptive LCP formulation for the compressible Navier–Stokes equations

This paper presents a polynomial-adaptive lifting collocation penalty (LCP) formulation for the compressible Navier–Stokes equations. The LCP formulation is a high-order nodal scheme in differential form. This format, although computationally efficient, complicates the treatment of non-uniform polynomial approximations. In Cagnone and Nadarajah (2012) [9], we proposed to circumvent this difficulty by employing specially designed elements inserted at the interface where the interpolation degree varies. In the present study we examine the applicability of this approach to the discretization of the Navier–Stokes equations, with focus put on the treatment of the viscous fluxes. The stability of the scheme is analyzed with the scalar diffusion equation and the merits of the approach are demonstrated with various p-adaptive simulations.