A Face-Centred Finite Volume Method for Laminar and Turbulent Incompressible Flows: Development and Application

Core Concepts

The author introduces a novel face-centred finite volume method for simulating laminar and turbulent incompressible flows, achieving accurate predictions of engineering quantities on unstructured meshes.

Abstract

This work presents a new face-centred finite volume (FCFV) solver for simulating laminar and turbulent viscous incompressible flows. The method avoids gradient reconstruction, making it insensitive to mesh quality. It accurately predicts engineering quantities like drag and lift. The FCFV formulation is applied to various problems including solid mechanics, heat transfer, and viscous flows. The study compares monolithic and staggered solution strategies for the RANS-SA system.
The content discusses the governing equations of incompressible RANS coupled with the negative SA turbulence model. It details the integral form of local problems enforcing mass conservation and momentum equations cell-by-cell. The global problem ensures continuity of inter-cell fluxes across internal interfaces.
Numerical examples include Couette flow testing optimal convergence under mesh refinement, showing similar accuracy on regular and distorted meshes. Lid-driven cavity flow assesses different convection stabilizations' accuracy on regular and distorted triangular meshes, demonstrating first-order convergence as the mesh refines.

Stats

Re = 1 (Reynolds number)
Meshes: 700x700 cells (reference solution), varying sizes for convergence studies

Quotes

"The resulting method achieves first-order convergence of velocity, pressure, and key engineering quantities."
"The FCFV method accurately predicts drag, lift, and other important parameters on unstructured meshes."

Key Insights Distilled From

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

by Luan M. Viei... at arxiv.org 03-05-2024

https://arxiv.org/pdf/2403.01496.pdf

Deeper Inquiries

How does the FCFV method compare to traditional cell-centered or vertex-centered finite volume techniques

The Face-Centered Finite Volume (FCFV) method differs from traditional cell-centered or vertex-centered finite volume techniques in several key aspects.

Gradient Reconstruction: In traditional methods, such as cell-centered or vertex-centered FV, a reconstruction of the gradient of the solution is required. This can lead to accuracy loss, especially in the presence of highly distorted cells. The FCFV method avoids this by directly working with face variables, making it insensitive to mesh quality.

Hybrid Discretization: FCFV can be seen as a hybridizable discontinuous Galerkin (HDG) method using the lowest order approximation for cell and face variables. This allows for efficient computations and accurate results on unstructured meshes.

Stabilizations: The formulation of convective stabilizations in FCFV is different from traditional methods and can impact the accuracy and stability of simulations significantly.

Accuracy on Distorted Meshes: Traditional methods may struggle with accuracy when dealing with distorted meshes, while FCFV has shown robustness even in such scenarios due to its unique approach.

What are the implications of using different convective stabilizations in numerical simulations

The choice of convective stabilization plays a crucial role in numerical simulations:

Accuracy vs Stability: Different stabilizations offer varying trade-offs between accuracy and stability.

Impact on Solution Quality: The type of stabilization used can affect how well the numerical scheme captures complex flow phenomena like shocks or vortices.

Computational Efficiency: Some stabilizations may require more computational resources but provide better results under certain conditions.

Mesh Sensitivity: Certain stabilizations might handle mesh distortion better than others, impacting simulation outcomes.

How does mesh distortion affect the accuracy of predictions in fluid dynamics simulations

Mesh distortion can have significant implications for fluid dynamics simulations:
1.Solution Accuracy: Highly distorted meshes can lead to inaccuracies in predictions due to interpolation errors across irregular cells.
2Convergence Rates: Mesh distortion may affect convergence rates, requiring finer grids or adaptive mesh refinement strategies for accurate results.
3Numerical Stability: Distorted meshes could introduce instabilities into the simulation that impact solution behavior over time steps
4Boundary Effects: Mesh distortions near boundaries could alter boundary layer characteristics affecting overall flow patterns and quantities predicted by simulations