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

• Published in: Journal of computational physics Vol. 233; pp. 324 - 338
• Main Authors: Cagnone, J.S., Vermeire, B.C., Nadarajah, S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 15.01.2013; Elsevier
• Subjects: Approximation; Compressible Navier–Stokes equations; Computational efficiency; Computational techniques; Exact sciences and technology; Fluid flow; Formulations; High-order methods; Interpolation; Lifting-collocation-penalty formulation; Liquid crystal polymers; Mathematical analysis; Mathematical methods in physics; Physics; Polynomial refinement; Scalars; Compressible Navier–Stokes equations; Polynomial refinement; Lifting-collocation-penalty formulation; High-order methods; Interpolation; Discretization; Differential form; Polynomial approximation; Diffusion equation; Calculation; Navier-Stokes equations; Calculation methods; Compressible Navier-Stokes equations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2012.08.053

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.