A non-oscillatory face-centred finite volume method for compressible flows

TL;DR

This paper introduces a face-centred finite volume method for compressible flows that is non-oscillatory, mesh-insensitive, and capable of accurately capturing sharp discontinuities without shock capturing techniques.

Contribution

The FCFV method defines unknowns at face barycentres, uses hybridisation to eliminate cell degrees of freedom, and inherently handles discontinuities without oscillations or gradient reconstruction.

Findings

Provides first-order accurate conservative quantities

Insensitive to mesh quality and distorted cells

Capable of capturing sharp discontinuities non-oscillatory

Abstract

This work presents the face-centred finite volume (FCFV) paradigm for the simulation of compressible flows. The FCFV method defines the unknowns at the face barycentre and uses a hybridisation procedure to eliminate all the degrees of freedom inside the cells. In addition, Riemann solvers are defined implicitly within the expressions of the numerical fluxes. The resulting methodology provides first-order accurate approximations of the conservative quantities, i.e. density, momentum and energy, as well as of the viscous stress tensor and of the heat flux, without the need of any gradient reconstruction procedure. Hence, the FCFV solver preserves the accuracy of the approximation in presence of distorted and highly stretched cells, providing a solver insensitive to mesh quality. In addition, FCFV is capable of constructing non-oscillatory approximations of sharp discontinuities without resorting to shock capturing or limiting techniques. For flows at low Mach number, the method is robust and is capable of computing accurate solutions in the incompressible limit without the need of introducing specific pressure correction strategies. A set of 2D and 3D benchmarks of external flows is presented to validate the methodology in different flow regimes, from inviscid to viscous laminar flows, from transonic to subsonic incompressible flows, demonstrating its potential to handle compressible flows in realistic scenarios.