Development of an algebraic fractional step scheme for the primitive formulation of the compressible Navier-Stokes equations

Abstract

In this work we address the compressible Navier-Stokes equations written in the so-called primitive formulation. The proposed methodology is a finite-element solver based on a fractional step scheme in time, which allows to uncouple the calculation of the problem unknowns providing important savings in computational cost. In addition, we include a stabilization technique within the Variational Multi-Scale framework and, in particular, we consider orthogonal and dynamic definitions for the subscales. In order to overcome any wave reflections which may arise in aeroacoustic simulations at the low compressibility regime, we present a method for enforcing boundary conditions based on a combination of a zero order non-reflecting condition plus the weak imposition of Dirichlet boundary conditions over the external contours. Several representative benchmark flow simulations are performed, which demonstrate the suitability of the proposed algorithm for the subsonic regime.