Futuristic aircraft wing transforming with adaptive mesh technology

Elasticity Algorithm: Enhancing Aircraft Design with Adaptive Mesh Technology

Avery Sinclair in Tech & Innovation June 2025 • 5 min read.

"Discover how a new quality-preserving algorithm for multi-element unstructured meshes can revolutionize aerodynamic simulations and design optimization, reducing design time and improving aircraft performance."

In the dynamic world of computational fluid dynamics (CFD), the ability to accurately simulate systems with moving parts is crucial. From predicting aircraft performance to optimizing designs, CFD relies on sophisticated mesh movement algorithms. These algorithms adjust the computational grid as components move, ensuring accurate and reliable simulations. However, creating meshes that capture complex geometric features and maintain quality throughout the simulation remains a significant challenge, especially when dealing with mixed element types. This challenge is particularly acute in the design optimization of high-lift systems, where unstructured meshes are preferred for their ability to conform to intricate shapes.

A new study addresses this challenge by introducing a quality-preserving linear elasticity mesh movement algorithm tailored for multi-element unstructured meshes. This algorithm adaptively stiffens mesh elements based on their quality, ensuring that the mesh maintains its integrity even as components move. By defining element quality as the condition number of the coordinate mapping, the algorithm can handle elements of arbitrary shape and size. This innovative approach promises to improve the success rate of implicit flow solvers on moved meshes, leading to more accurate and efficient aerodynamic simulations.

The implications of this research extend beyond mere simulation accuracy. By enhancing the robustness and efficiency of mesh movement, the algorithm accelerates the design optimization process, allowing engineers to explore more design options and converge on optimal solutions faster. This breakthrough has the potential to transform how aircraft are designed, tested, and optimized, offering a competitive edge in the aerospace industry.

What is Linear Elasticity Mesh Movement?

Futuristic aircraft wing transforming with adaptive mesh technology

At the heart of this innovation is the concept of treating the entire mesh as a solid material with a Young's modulus (E), which represents its stiffness or resistance to deformation. Typically, this modulus is allowed to vary spatially based on metrics related to the local mesh element. For instance, smaller elements are made more resistant to distortion, preventing them from becoming inverted or developing negative volume. This is crucial for maintaining the validity and accuracy of the simulation.

However, simply preventing mesh elements from collapsing isn't enough. The quality of the mesh—how well-shaped the elements are—also plays a vital role in the accuracy and stability of the CFD algorithm. Several metrics, such as aspect ratio and internal angle, have been used to quantify element quality. The problem is that these metrics aren’t universally applicable across different element types (e.g., prisms, tetrahedra) or directly relevant to the CFD algorithm's performance. So, how can we ensure consistent quality across a heterogeneous mesh?

Algebraic methods: Simple and fast but not robust for complex 3D geometries.
Delaunay graph methods: Alternative approaches to mesh deformation.
Spring analogy method: Can be robust but computationally expensive.
Radial basis functions: A more recent development that can be less expensive than linear elasticity.
Explicit interpolation: Similar to radial basis functions.
Linear elasticity: Among the most widely used due to its robustness, though it can be CPU-intensive.

The study introduces a novel approach by incorporating an element quality metric into Young's modulus. This metric, based on the condition number of the geometric mapping from each mesh element to its original shape, ensures that the mesh mover preserves the mesh quality without favoring specific element types. The algorithm adaptively stiffens each mesh element in multiple increments, using the following formula: Ee,i = (1 / Ve,i) Πj=1i [Φe,j]rj Where Φ is the quality metric, r is the fraction of total deflection, and V is the volume. This adaptive stiffening mechanism effectively maintains element quality throughout the mesh movement process.

Real-World Applications and Future Directions

To validate the algorithm's effectiveness, the researchers applied it to two practical three-dimensional test cases: the NASA Common Research Model (CRM) wing-body and the Bombardier Research Aircraft (BRAC) wing and flap geometry. The results demonstrated that the adaptive stiffening algorithm allowed for larger mesh movements and improved the flow solver's convergence compared to traditional volume-based stiffening. The flow solver parameters were chosen conservatively to attempt to converge as many cases as possible. However, no attempt was made to optimize the solver parameters for the set of cases investigated. These findings have significant implications for the aerospace industry, where accurate and efficient CFD simulations are essential for optimizing aircraft designs. By enabling larger and more complex mesh movements while preserving mesh quality, the algorithm paves the way for more comprehensive design exploration and improved aircraft performance. The researchers also suggest that future work could explore alternative formulations for Young's modulus and investigate the use of larger quality metrics to further enhance the algorithm's robustness. Additionally, the integration of this mesh movement algorithm with gradient-based optimization techniques holds promise for automating and accelerating the design optimization process.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.2514/1.j057463, Alternate LINK

Title: Quality-Preserving Linear Elasticity Mesh Movement Algorithm For Multi-Element Unstructured Meshes

Subject: Aerospace Engineering

Journal: AIAA Journal

Publisher: American Institute of Aeronautics and Astronautics (AIAA)

Authors: David A. Brown, Siva Nadarajah, Hong Yang, Patrice Castonguay, Hassan Raiesi, Kurt Sermeus, Patrick Germain

Published: 2019-02-01

Everything You Need To Know

What is the primary challenge addressed by the linear elasticity mesh movement algorithm in aircraft design?

The primary challenge addressed by the algorithm is maintaining mesh quality and integrity during the simulation of moving parts in computational fluid dynamics (CFD). This is particularly crucial when simulating complex geometries and using unstructured meshes, like those preferred for high-lift systems. The algorithm ensures the mesh doesn't distort excessively, allowing for more accurate and reliable simulations, especially when dealing with mixed element types. This helps in optimizing designs and improving aircraft performance.

How does the adaptive stiffening mechanism within the linear elasticity algorithm work to preserve mesh quality?

The adaptive stiffening mechanism works by modifying Young's modulus (E) of each mesh element based on its quality. The quality metric, based on the condition number of the geometric mapping, is used to adaptively stiffen mesh elements in multiple increments. The formula 'Ee,i = (1 / Ve,i) * Πj=1i [Φe,j]rj' is used, where Φ is the quality metric, r is the fraction of total deflection, and V is the volume. This ensures that elements maintain their shape and integrity even when components move, thereby preventing mesh distortion and maintaining simulation accuracy. This approach does not favor specific element types.

What are the real-world applications and benefits of this linear elasticity mesh movement algorithm in the aerospace industry?

In the aerospace industry, the algorithm offers several benefits. It improves the accuracy and efficiency of CFD simulations, crucial for optimizing aircraft designs. By enabling larger and more complex mesh movements while preserving mesh quality, the algorithm enhances design exploration and improves aircraft performance. This is demonstrated in practical test cases like the NASA CRM wing-body and the BRAC wing and flap geometry, where it allowed for larger mesh movements and improved the flow solver's convergence compared to traditional methods, leading to faster design cycles and potentially more fuel-efficient and effective aircraft.

What is Young's modulus (E) and how does it relate to this mesh movement algorithm?

Young's modulus (E) represents the stiffness or resistance to deformation of a material. In this algorithm, the mesh is treated as a solid material, and Young's modulus is used to control how mesh elements respond to movement. The algorithm adaptively adjusts Young's modulus of mesh elements based on a quality metric. This adaptive adjustment helps maintain the quality of the mesh during the simulation, preventing elements from distorting or inverting, which is crucial for accurate simulations. The novel approach incorporates an element quality metric into Young's modulus to maintain mesh quality without favoring specific element types. Specifically, the modulus is modified based on the condition number of the geometric mapping of each mesh element.

What are the potential future directions for this research, and what impact could they have on aircraft design?

Future research could explore alternative formulations for Young's modulus and investigate larger quality metrics to further enhance the algorithm's robustness. Moreover, integrating this mesh movement algorithm with gradient-based optimization techniques could automate and accelerate the design optimization process. These advancements could lead to more efficient design cycles, better aircraft performance, and the ability to explore a broader range of design options. This could transform how aircraft are designed, tested, and optimized, offering a significant competitive advantage in the aerospace industry, driving innovation in areas like fuel efficiency, structural integrity, and aerodynamic performance.