JuliaCon Local Paris 2025

Solving partial differential equations with Bcube.jl
2025-10-02 , Jean-Baptiste Say Amphitheater
Language: English

Bcube.jl is a new open-source Julia package developed at ONERA to solve PDEs on unstructured meshes using finite element and discontinuous Galerkin methods. It enables flexible, efficient, and unified multi-physics simulations. This talk presents the package's philosophy, architecture, and capabilities through diverse examples, and shares insights on using Julia in an industrial research context.


The Multi-Physics Department for Energetics at ONERA focuses on aerospace applications such as propulsion systems, laminar–turbulent transition, and icing, among others. These phenomena are typically modeled by systems of partial differential equations (PDEs) with diverse mathematical structures. As a result, they are often solved using dedicated solvers with specific numerical methods. However, this fragmented approach complicates the development of strong multi-physics couplings and hinders the mutualization of numerical efforts.
To address this challenge, we have developed Bcube.jl, an open-source Julia package designed at ONERA for solving PDEs on unstructured meshes. Similar to packages like Gridap.jl and Ferrite.jl, Bcube.jl provides a user-friendly and efficient framework for discretizing PDEs using either the finite element method or the discontinuous Galerkin method. In this talk, we will present the overall philosophy behind Bcube.jl as well as its core architecture.
The presentation will include illustrative examples across various applications—from the Euler equations around an airfoil to the resolution of PDEs on curved surfaces such as those arising in shallow water models. These examples will demonstrate both the usability and versatility of the library.
We will conclude with perspectives on the future development of Bcube.jl, particularly in the context of high-performance computing and advanced numerical methods. Finally, we will share reflections on adopting Julia in a research institution like ONERA, which traditionally develops software for the aerospace industry.

Maxime Bouyges is a Research Engineer in Fluid Dynamics at ONERA's Department of Multi-Physics for Energetics. Commencing his career in 2013, he completed a PhD focusing on stability analysis of complex flows within solid rocket engines. Subsequently, he joined the Multiphase Flow Research Team, contributing to the development of the CEDRE-FILM solver - a parallel 3D surface solver tailored for shallow-water and icing applications. Currently, his work encompasses the advancement of physical models and numerical methods, primarily within the realm of icing phenomena.

Ghislain Blanchard is a research engineer in fluid dynamics at ONERA’s Department of Multi-Physics for Energetics since 2015. His research interests include the development of numerical methods for multi-physics simulations and high performance computing.