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

Abstract

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.

Samuel Parada gratefully acknowledges the support received from the Agència de Gestió d'Ajuts Universitaris i de Recerca through the predoctoral FI grant 2019-FI-B-00607. Joan Baiges gratefully acknowledges the support of the Spanish Government through the Ramón y Cajal grant RYC-2015-17367. Ramon Codina gratefully acknowledges the support received from the ICREA Acadèmia Research Program of the Catalan Government. This work was partially funded through the TOP-FSI: RTI2018-098276-B-I00 project of the Spanish Government. CIMNE is a recipient of a “Severo Ochoa Programme for Centers of Excellence in R&D” grant (CEX2018-000797-S) by the Spanish Government.

Peer Reviewed

Postprint (author's final draft)