An OpenFOAM face-centred solver for incompressible flows robust to mesh distortion

TL;DR

The paper addresses mesh-induced errors in cell-centered finite-volume methods for incompressible flows and proposes integrating a robust face-centered finite-volume (FCFV) solver into OpenFOAM. By using a mixed-hybrid formulation with a hybrid velocity on face barycentres and a custom sparsity structure, the method avoids gradient reconstruction and enhances stability on non-orthogonal, skewed, and stretched meshes. Numerical benchmarks (Couette, lid-driven cavity, and an oscillator) show that FCFV delivers first-order convergence for velocity and pressure, maintains accuracy under mesh distortion, and outperforms standard CCFV solvers. The work demonstrates that FCFV in OpenFOAM can handle convection-dominated incompressible flows with improved robustness and reduced mesh-generation constraints.

Abstract

This work presents an overview of mesh-induced errors commonly experienced by cell-centred finite volumes (CCFV), for which the face-centred finite volume (FCFV) paradigm offers competitive solutions. In particular, a robust FCFV solver for incompressible laminar flows is integrated in OpenFOAM and tested on a set of steady-state and transient benchmarks. The method outperforms standard simpleFoam and pimpleFoam algorithms in terms of optimal convergence, accuracy, stability, and robustness. Special attention is devoted to motivate and numerically demonstrate the ability of the FCFV method to treat non-orthogonal, stretched, and skewed meshes, where CCFV schemes exhibit shortcomings.

Figures (12)

• Figure 1: Angle $\theta$ between the vector $\bm{d}$ connecting the centroids of cells $\Omega_e$ and $\Omega_{\ell}$ and the vector $\bm{n}_{j}$ normal to face $\Gamma_{\!e,j}$.
• Figure 2: Distance $\bm{s}$ between the barycentre $\bm{x}_{j}$ of face $\Gamma_{\!e,j}$ and its intersection $\bm{\tilde{x}_{j}}$ with vector $\bm{d}$ connecting the centroids of cells $\Omega_e$ and $\Omega_{\ell}$.
• Figure 3: Computational stencil of the discretisations on a mesh of quadrilateral cells. Red: node under analysis. Blue: nodes employed in the discretisation. Gray: inactive nodes.
• Figure 4: Second level of refinement of the computational meshes for the Couette flow.
• Figure 5: Mesh convergence of the $\mathcal{L}^2$ errors for the Couette flow.

Theorems & Definitions (1)

• Remark 1