A non-oscillatory face-centred finite volume method for compressible flows. (15th March 2022) - Vila-Pérez, Jordi; Giacomini, Matteo; Sevilla, Ruben; Huerta, Antonio
Abstract: This work presents a 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. Highlights: Face-centred finite volume formulation for compressible flows, robust in the incompressible limit. First-order accuracy of viscous stress and heat flux, without gradient reconstruction. FV solver insensitive to mesh quality and robust in the presence of distorted and stretched cells. Non-oscillatory approximation of sharp discontinuities, without shock capturing or limiting techniques. Comprehensive numerical validation, from inviscid to viscous laminar flows, from transonic to subsonic incompressible flows.