Benchmarking the face-centred finite volume method for compressible laminar flows

TL;DR

This paper evaluates the face-centred finite volume (FCFV) method's robustness and accuracy for simulating compressible laminar flows across various regimes, demonstrating its efficiency and reliability on distorted meshes and complex geometries.

Contribution

The study provides a comprehensive benchmarking of the FCFV method, highlighting its first-order accuracy, insensitivity to mesh distortion, and superior performance in high Mach number flows without carbuncle effects.

Findings

Accurately predicts viscous stress and heat flux on distorted meshes.

Achieves errors below 5% for quantities like drag, lift, and heat transfer.

Handles a wide Mach number range, including incompressible limit, without pressure correction.

Abstract

Purpose: This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks. Design/methodology/approach: The work presents a detailed comparison with reference solutions published in the literature -- when available -- and numerical results computed using a commercial cell-centred finite volume software. Findings: The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%. Originality/value: The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.