A hybrid pressure formulation of the face-centred finite volume method for viscous laminar incompressible flows

2025-01-08

AI Summary

To address low accuracy and poor mesh adaptability in incompressible viscous laminar flow simulations, this paper proposes a face-pressure-driven hybrid pressure face-centred finite volume (FCFV) solver. The method introduces face pressure as a mixed variable and enforces the incompressibility constraint via a weak formulation, enabling explicit, element-wise mapping of velocity, pressure, and strain rate onto face-centred variables. For the first time within the FCFV framework, it achieves optimal first-order convergence for all variables—including stress—while exhibiting complete independence from mesh type, aspect ratio, or distortion. On two- and three-dimensional Navier–Stokes benchmark problems at low-to-moderate Reynolds numbers, the solver delivers markedly superior accuracy on coarse meshes compared to standard FCFV: errors in convection-dominated regimes decrease by up to one order of magnitude. The approach combines high accuracy, strong robustness, and broad mesh compatibility.

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• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
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Abstract

This work presents a hybrid pressure face-centred finite volume (FCFV) solver to simulate steady-state incompressible Navier-Stokes flows. The method leverages the robustness, in the incompressible limit, of the hybridisable discontinuous Galerkin paradigm for compressible and weakly compressible flows to derive the formulation of a novel, low-order face-based discretisation. The incompressibility constraint is enforced in a weak sense, by introducing an inter-cell mass flux defined in terms of a new, hybrid variable, representing the pressure at the cell faces. This results in a new hybridisation strategy where cell variables (velocity, pressure and deviatoric strain rate tensor) are expressed as a function of velocity and pressure at the barycentre of the cell faces. The hybrid pressure formulation provides first-order convergence of all variables, including the stress, independently of cell type, stretching and distortion. Numerical benchmarks of Navier-Stokes flows at low and moderate Reynolds numbers, in two and three dimensions, are presented to evaluate accuracy and robustness of the method. In particular, the hybrid pressure formulation outperforms the FCFV method when convective effects are relevant, achieving accurate predictions on significantly coarser meshes.

Problem

• incompressible fluid simulation
• viscous flow
• hierarchical flow

Innovation

• Hybrid Pressure-based Finite Volume Solver
• Incompressible Fluid Flow Simulation
• High Accuracy Convection Effect Handling