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Modeling & Simulation

Mediathena et Julie Dugast - 6/11/2020

“Smart” 3D meshing supports industry

The Gamma team from the Inria Saclay-Île-de-France research centre has displayed its expertise in computing through the adaptation of 3D meshing. This method is used by manufacturers to model and perform digital simulations of their products’ physical behaviour. This year, the team is also organising Workshop Tetrahedron VI, the sixth edition of an international triennial aimed at aligning academic research with manufacturers’ needs for meshing technology.

For over 20 years, Inria has been exploring advanced meshing technology and digital methods for industrial simulations. Since 1996, the Gamma team has been developing specific expertise in automatic meshing generation and advanced methods. It organised the Workshop Tetrahedron VI. Nearly one hundred people attended the event held on the Saclay campus in early October.

Advanced meshing methods for increased power and precision

Numerous industrial applications require the use of digital simulations to assess a product’s interactions with its environment, particularly for design optimisation. The aeronautics industry, for example, uses it to decrease sonic “boom”,1 the oil industry to reinforce offshore platforms’ resistance to ocean currents, and the propulsion industry to improve the flow of fluids in an engine. The list could go on, as there is a wide range of examples, but all with a common need: reliable and precise modelling that can take complex geometries into account and be calculated rapidly (from a few minutes to a few hours). The solution lies in meshing methodology.

Meshing accurately reproduces the shape of an object – or volume – by breaking it down into juxtapositions of simple geometrical elements like triangles and/or quadrilaterals, or, in the case of 3D studies, with tetrahedrons2 and/or hexahedrons.3 One of the Gamma researchers’ priorities is to improve this methodology and technology in order to achieve greater effectiveness and precision in digital industrial simulations. They have developed an automated process using calculations to define optimal meshing for a given criterion that can automatically specify the shape and size of the mesh composing it.

“We have developed a mesh adaptation algorithm in order to determine the mesh that should be generated for the best solution to the given problem,”explains Frédéric Alauzet, head of the Gamma team. “Using a computer-aided design (CAD) representing a geometric model, we generated an initial mesh without any preconceived ideas about the problem in question. The algorithm then performs an iterative process. It calculates the solution using the current mesh, estimates the error in this solution, then specifies the shape and size of each element in the new mesh in order to reduce this error for a number of given elements. This process is repeated until “convergence” is reached, which means until the mesh and solution cannot progress any further. In summary, adapting the mesh to the physical problem makes it possible to obtain the best possible digital solution (i.e. the smallest error) for a mesh size (i.e. a number of elements) given by the user.  Since we are able to quantify the error in the digital solution, this is a first step towards certifying digital simulations.”

The algorithm created by Gamma scientists, for example, can model an object by discretisation,4 with “large” mesh for an area where liquid flows smoothly, and “smaller” mesh featuring shapes better suited to an area where the liquid’s behaviour varies greatly and is dependent on details.

With the current calculations, the meshing is composed of tens of millions to billions of elements. Considering that the cost of digital simulation depends on the size of the mesh5, it is easy to imagine the economic impact of such algorithms: less calculation time, less memory consumed, and less data stored.

In order to master this mesh that is both anisotropic (does not have the same physical configuration in every direction) and adaptive (“made to measure” based on the physical phenomena to be simulated), the Gamma team includes experts covering all the necessary aspects: the meshing itself as well as numerical solvers to achieve the simulations requested by industrials,   the visualisation of the meshing and the solutions.

Co-developed applications

Workshop Tetrahedron is an essential professional gathering for academic researchers and industry professionals. Researchers constantly rely on the actual needs of industry professionals to advance their work. “It is essential for us to be in direct contact with the end users of our work. The knowledge of their needs and the feedback they provide enable us to carry out the basic research needed to provide tools that are complementary and more refined,”Frédéric Alauzet explains. “We are thrilled to see this workshop bringing together as many industry professionals as it does European, American, Russian and Japanese academic researchers, because we want to create real connections between meshing stakeholders and create a dynamic environment by welcoming new speakers every three years.” They met this goal this year, with 80% new speakers sharing their experience!

Thanks to their industrial partnerships, such as with French SMEs Distene and Lemma, Gamma researchers have already improved several aspects of mesh technologies. The industrial partners used their own calculation procedures to integrate the results achieved or made them available to their customers . These results were also shared with a wider audience, since they can be reused and adapted in several areas.

Over the next few years, the Gamma research programme, led by Frédéric Alauzet, should continue to provide innovative solutions for every stage in the adaptive digital calculation process. Its research will focus on large mesh sizes , by relying on calculations using parallelism and curved meshing for greater accuracy, as well as the certification of calculations with the quantification of numerical errors caused by discretisation.


1 sonic “boom”: explosion caused by objects moving in the atmosphere at speeds exceeding the speed of sound.

2 Tetrahedrons: geometric elements composed of 4 triangular faces.

3 Hexahedrons: geographic elements composed of 6 faces.

4 “Discretise”: continuously replace something (a surface, volume, etc.) with a succession of small mesh (simple geometric elements)  

5 Mesh size: the number of elements composing the mesh.

Keywords: Industrial partnership International Solvers 3D meshing Digital simulations