ECCOMAS 2024

A face-centered finite volume method for laminar and turbulent incompressible flows

  • Giacomini, Matteo (Universitat Politècnica de Catalunya)
  • Vieira, Luan (Universitat Politècnica de Catalunya)
  • Cortellessa, Davide (Universitat Politècnica de Catalunya)
  • Sevilla, Rubén (Swansea University)
  • Huerta, Antonio (Universitat Politècnica de Catalunya)

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CFD encounters continuous challenges from both scientific and engineering perspectives. Modeling, particularly in relation to turbulence and chemical reactions, remains a persistent challenge. However, complex geometrical configurations are likely more limiting in the present scenario. They present a significant hurdle in advanced engineering flow simulations, as mesh generation causes delays in time-to-market due to solver sensitivity to mesh quality. A solution is imperative: robust solvers that are less sensitive to cell distortion and stretching, capable of efficiently tackling large-scale problems on unstructured meshes. Finite volume methods are widely used in CFD simulations for industrial problems due to their robustness and efficient implementations. However, a drawback of current cell-centered (CCFV) and vertex-centered (VCFV) strategies is their requirement for high-quality meshes, which are exceptionally costly in terms of specialized technician person-hours for generation. The accuracy of both CCFV and VCFV is indeed compromised when dealing with distorted and stretched cells. On the contrary, the face-centered (FCFV) offers a framework that is less susceptible to mesh quality issues, maintaining accuracy in approximations even when dealing with complex unstructured meshes containing highly distorted and stretched cells. The FCFV method establishes unknowns at the face barycenter and employs hybridization to eliminate degrees of freedom within each cell because, in essence, it is an extension of the Hybridizable Discontinuous Galerkin method to piecewise constant approximation in each cell. This methodology yields first-order accurate approximations of the viscous stress tensor without the necessity for gradient reconstruction procedures. Additionally, FCFV proves to be robust for incompressible laminar and turbulent flows, eliminating the need for specific pressure correction strategies. The stabilization for convection is grounded in Riemann solvers, which are implicitly defined within the expressions of the numerical fluxes. Notably, this strategy has undergone testing across a diverse range of elements, including prisms and pyramids. It is worth mentioning that hexahedra with non-planar faces, which typically require special treatment with standard FV methods, can also be effectively utilized. To validate the methodology laminar and turbulent incompressible viscous flows benchmarks will be presented.