Finite volume method for the solution of flow on distorted meshes

Abstract

Purpose

To improve flow solutions on meshes with cells/elements which are distorted/ non‐orthogonal.

Design/methodology/approach

The cell‐centred finite volume (FV) discretisation method is well established in computational fluid dynamics analysis for modelling physical processes and is typically employed in most commercial tools. This method is computationally efficient, but its accuracy and convergence behaviour may be compromised on meshes which feature cells with non‐orthogonal shapes, as can occur when modelling very complex geometries. A co‐located vertex‐based (VB) discretisation and partially staggered, VB/cell‐centred (CC), discretisation of the hydrodynamic variables are investigated and compared with purely CC solutions on a number of increasingly distorted meshes.

Findings

The co‐located CC method fails to produce solutions on all the distorted meshes investigated. Although more expensive computationally, the co‐located VB simulation results always converge whilst its accuracy appears to grace‐fully degrade on all meshes, no matter how extreme the element distortion. Although the hybrid, partially staggered, formulations also allow solutions on all the meshes, the results have larger errors than the co‐located vertex based method and are as expensive computationally; thus, offering no obvious advantage.

Research limitations/implications

Employing the ability of the VB technique to resolve the flow field on a distorted mesh may well enable solutions to be obtained on complex meshes where established CC approaches fail

Originality/value

This paper investigates a range of cell centred, vertex based and hybrid approaches to FV discretisation of the NS hydrodynamic variables, in an effort characterize their capability at generating solutions on meshes with distorted or non‐orthogonal cells/elements.

Citation

McBride, D., Croft, N. and Cross, M. (2007), "Finite volume method for the solution of flow on distorted meshes", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 No. 2, pp. 213-239. https://doi.org/10.1108/09615530710723975