A review of aerodynamic flow models, solution methods and solvers – and their applicability to aircraft conceptual design

This page presents the literature study I have conducted in preparation for my graduation research at Delft University of Technology. Here, you can download various versions of my literature study report and larger size images.


This literature study report is written in preparation for a subsequent graduation research project, that aims to develop a methodology for uncertainty quantification in (aerodynamic) models, in order to contribute to improve decisions made in the conceptual aircraft design process. In the current text, the assumptions, simplifications and limitations of various aerodynamic solvers have been investigated, as well as their performance compared. A more fundamental discussion of flow models (from Navier-Stokes to Laplace’s equation) and non-linear (FDM, FEM, FVM) and linear (LLT, VLM, panel methods) solution methods precede an analysis of 11 solvers of different fidelity levels.

Of the two-dimensional codes, XFOIL (panel method and boundary layer model), VGK (full potential FDM and BL model), MSES (Euler FVM and BL model) and ARC2D (thin-layer NS using FDM) were investigated. In three dimensions, the research included vortex lattice methods VLM and Tornado, VSAERO (panel method and BL model), MATRICS-V (full potential FVM and BL model) and SU2 (Euler, inviscid NS and turbulent RANS using FVM or FEM). XFLR5 and Q3D, combining 2D boundary layer models with 3D linear potential codes, were classified as ‘hybrid’ solvers and analysed. Given their different flow models, these codes most notably vary in terms of including viscosity, the applicable Mach number range and limitations to geometry modelling.

Unsurprisingly, it was concluded that the higher-fidelity codes generally match experimental results best. In 2D codes, predicting shock strength and shock location were found to be most difficult. The 3D codes mostly differentiated themselves based on the geometric detail that could be modelled. In this case, higher-fidelity models outperformed lower-fidelity codes. Problems with accurately predicting transition and separation (insofar supported by the computational tool in question) were – to a greater or lesser extent – seen throughout the entire range of solvers considered.

On the other hand, these higher-fidelity codes come at an increased computational cost – both directly in terms of computer time and indirectly because of preparatory work, such as geometry modelling and meshing. Although various authors see application of more advanced CFD codes earlier in the (conceptual) design process as a key towards enabling technologies such as early MDO, others believe conceptual design should remain focused on the high-level parameters and not pay too much attention the details. Also, scholars feel that current (drafting-based) CAD-software suitable for generating detailed enough geometries required by advanced simulations are unsuitable for rapid design and iteration common in conceptual design. In conclusion, it is felt a lower limit is set by the requirement that a solver should be able to definitively distinguish between concepts and a (currently fairly stringent) upper limit by computational cost and geometry requirements.


Below you find various versions of the report, suitable for either screen viewing (one-sided, i.e. equal left and right margins) or printing (two-sided, i.e. larger inner margin suitable for binding). The PDF-documents are about 8MB each.

Overviews of aerodynamic flow models and solvers

Included in the report are two infographic-like overviews of aerodynamic flow models (Figure 2.1) and aerodynamic solvers (Figure 6.1). The PDF-documents are less than 100 kB each.

The first indicates the relevant assumptions of various flow models, which are hierarchically ordered by fidelity level. The second indicates what flow model(s) and what solution method(s) are used in a variety of solvers and highlights some characteristics, such as the use cases and popularity. Using the link below, you can download these figures in a larger size.

Type Studieopdracht
Cijfer 9/10
Looptijd 06/2018 - 10/2018