A VMS-based fractional step technique for the compressible Navier-Stokes equations using conservative variables

In this paper we address the compressible Navier-Stokes equations written in the so-called conservative formulation. In particular, we focus on the possibility of uncoupling the computation of the problem unknowns, namely, density, linear momentum and total energy, a technique usually labeled as fractional step method, which allows to reduce the associated computational cost. The proposed methodology is a finite-element solver supplemented with a stabilization technique within the Variational Multi-Scale framework. In this regard, we consider orthogonal and dynamic definitions for the subscales. This discretization in space shows an adequate stability, permitting in particular the use of equal interpolation for all variables in play. However, we complement it with a shock-capturing operator in order to solve problems involving shocks. Several representative benchmark flow simulations are performed, which demonstrate the suitability of the proposed algorithm for a vast range of regimes.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper addresses the compressible Navier-Stokes equations in the conservative formulation and focuses on the possibility of decoupling the computation of the problem unknowns. The proposed method, known as the fractional step method, reduces the computational cost. It utilizes a finite-element solver with a stabilization technique within the Variational Multi-Scale framework, considering orthogonal and dynamic definitions for the subscales. The discretization in space ensures stability and the use of equal interpolation for all variables. A shock-capturing operator is also added to solve problems involving shocks. The simulations demonstrate the suitability of the algorithm for various flow regimes.