Assessment of Implicit and Adaptive Mesh-free CFD Modelling

Abstract

This work presents detailed investigations of implicit and adaptive mesh-free CFD modelling approaches to alleviate laborious mesh generation in modern CFD processes. A least-square based mesh-free discretisation scheme was derived for the compressible RANS equations, and the implicit dual-time stepping was adopted for improved stability and convergence. The spatial accuracy and convergence properties were verified using 2D and 3D benchmark cases. The impact of irregular point distributions and various point collocation choices were then systematically investigated. The mesh-free scheme showed strong flexibility accommodating various point distributions and collocation configurations, but the modelling was sensitive to the regularity and reciprocity of the collocation, especially in critical flow regions, e.g. boundary layers. The mesh-free flexibility was exploited for adaptive modelling, and various adaptation strategies were assessed, combining different point refinement mechanisms and collocation search methods. Their performance was carefully evaluated using simulations of the isentropic vortex. The mesh-free modelling was then successfully applied to transonic RAE 2822 aerofoil simulations with automated point generation. A novel weighted pressure gradient metric prioritising high gradient regions with large point sizes was introduced to drive the adaptation. The mesh-free adaptation was found to effectively improve the shock resolution.