A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling

Evans, Ben; Smith, Ben; Walton, Sean; Taylor, Neil; Dodds, Martin; Zmijanovic, Vladeta

doi:10.3390/aerospace11040298

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A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling

Ben Evans

, Ben Smith, Sean Walton

, Neil Taylor, Martin Dodds, Vladeta Zmijanovic

Aerospace, Volume: 11, Issue: 4, Start page: 298

Swansea University Authors: Ben Evans , Sean Walton

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DOI (Published version): 10.3390/aerospace11040298

Abstract

In this paper, an optimisation procedure is introduced that uses a significantly cheaper, and CFD-free, objective function for aerodynamic optimisation than conventional CFD-driven approaches. Despite the reduced computational cost, we show that this approach can still drive the optimisation scheme...

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Published in:	Aerospace
ISSN:	2226-4310
Published:	MDPI AG 2024
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa70872

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A summary of the wave drag approximation in transonic and supersonic regimes is outlined along with the methodology for exploiting this theory on a typical CFD surface mesh to construct an objective function evaluation for a given geometry. The implementation is presented including notes on the considerations required to ensure stability, and error minimisation, of the numerical scheme. The paper concludes with the results from a number of (simple and complex geometry) examples of a drag-minimisation optimisation study and the results are compared with an approach using full-fidelity CFD simulation. The overall conclusions from this study suggest that the approach presented is capable of driving a geometry towards a similar shape to when using full-fidelity CFD at a significantly lower computational cost. 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spelling	2026-01-08T12:26:50.3635438 v2 70872 2025-11-10 A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling 3d273fecc8121fe6b53b8fe5281b9c97 0000-0003-3662-9583 Ben Evans Ben Evans true false 0ec10d5e3ed3720a2d578417a894cf49 0000-0002-6451-265X Sean Walton Sean Walton true false 2025-11-10 ACEM In this paper, an optimisation procedure is introduced that uses a significantly cheaper, and CFD-free, objective function for aerodynamic optimisation than conventional CFD-driven approaches. Despite the reduced computational cost, we show that this approach can still drive the optimisation scheme towards a design with a similar reduction in drag coefficient for wave drag-dominated problems. The approach used is ‘CFD-free’, i.e., it does not require any computational aerodynamic analysis. It can be applied to geometries discretised using meshes more conventionally used for ‘standard’ CFD-based optimisation approaches. The approach outlined in this paper makes use of the transonic area rule and its supersonic extension, exploiting a mesh-based parameterisation and mesh morphing methodology. The paper addresses the following question: ‘To what extent can an optimiser perform (wave) drag minimisation if using ‘area ruling’ alone as the objective (fitness) function measurement?’. A summary of the wave drag approximation in transonic and supersonic regimes is outlined along with the methodology for exploiting this theory on a typical CFD surface mesh to construct an objective function evaluation for a given geometry. The implementation is presented including notes on the considerations required to ensure stability, and error minimisation, of the numerical scheme. The paper concludes with the results from a number of (simple and complex geometry) examples of a drag-minimisation optimisation study and the results are compared with an approach using full-fidelity CFD simulation. The overall conclusions from this study suggest that the approach presented is capable of driving a geometry towards a similar shape to when using full-fidelity CFD at a significantly lower computational cost. However, it cannot account for any constraints, driven by other aerodynamic factors, that might be present within the problem. Journal Article Aerospace 11 4 298 MDPI AG 2226-4310 evolutionary optimisation; area ruling; wave drag; Sears–Haack 11 4 2024 2024-04-11 10.3390/aerospace11040298 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University Other The authors would like to acknowledge the support provided by Reaction Engines Ltd. and EPSRC under grant number EP/T517987/1 for provision of funding to support this work. 2026-01-08T12:26:50.3635438 2025-11-10T14:07:55.1046633 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Ben Evans 0000-0003-3662-9583 1 Ben Smith 2 Sean Walton 0000-0002-6451-265X 3 Neil Taylor 4 Martin Dodds 5 Vladeta Zmijanovic 6 70872__35923__889823b69df5478294040a87e4fe0143.pdf 70872.VoR.pdf 2026-01-08T12:25:18.5541525 Output 8147308 application/pdf Version of Record true © 2024 by the authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license. true eng https://creativecommons.org/licenses/by/4.0/
title	A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling
spellingShingle	A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling Ben Evans Sean Walton
title_short	A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling
title_full	A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling
title_fullStr	A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling
title_full_unstemmed	A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling
title_sort	A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling
author_id_str_mv	3d273fecc8121fe6b53b8fe5281b9c97 0ec10d5e3ed3720a2d578417a894cf49
author_id_fullname_str_mv	3d273fecc8121fe6b53b8fe5281b9c97_*_Ben Evans 0ec10d5e3ed3720a2d578417a894cf49_*_Sean Walton
author	Ben Evans Sean Walton
author2	Ben Evans Ben Smith Sean Walton Neil Taylor Martin Dodds Vladeta Zmijanovic
format	Journal article
container_title	Aerospace
container_volume	11
container_issue	4
container_start_page	298
publishDate	2024
institution	Swansea University
issn	2226-4310
doi_str_mv	10.3390/aerospace11040298
publisher	MDPI AG
college_str	Faculty of Science and Engineering
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department_str	School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
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description	In this paper, an optimisation procedure is introduced that uses a significantly cheaper, and CFD-free, objective function for aerodynamic optimisation than conventional CFD-driven approaches. Despite the reduced computational cost, we show that this approach can still drive the optimisation scheme towards a design with a similar reduction in drag coefficient for wave drag-dominated problems. The approach used is ‘CFD-free’, i.e., it does not require any computational aerodynamic analysis. It can be applied to geometries discretised using meshes more conventionally used for ‘standard’ CFD-based optimisation approaches. The approach outlined in this paper makes use of the transonic area rule and its supersonic extension, exploiting a mesh-based parameterisation and mesh morphing methodology. The paper addresses the following question: ‘To what extent can an optimiser perform (wave) drag minimisation if using ‘area ruling’ alone as the objective (fitness) function measurement?’. A summary of the wave drag approximation in transonic and supersonic regimes is outlined along with the methodology for exploiting this theory on a typical CFD surface mesh to construct an objective function evaluation for a given geometry. The implementation is presented including notes on the considerations required to ensure stability, and error minimisation, of the numerical scheme. The paper concludes with the results from a number of (simple and complex geometry) examples of a drag-minimisation optimisation study and the results are compared with an approach using full-fidelity CFD simulation. The overall conclusions from this study suggest that the approach presented is capable of driving a geometry towards a similar shape to when using full-fidelity CFD at a significantly lower computational cost. However, it cannot account for any constraints, driven by other aerodynamic factors, that might be present within the problem.
published_date	2024-04-11T05:33:50Z
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score	11.096068

A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling

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