Anisotropic meshes require robust schemes, especially when the element’s anisotropy can be about one million. Moreover, it is interesting to define the degrees of freedom and the sensors for mesh adaptation at the same location. In practice, both are at mesh nodes.
The finite volume formulation requires the definition of the control volumes around mesh nodes, leading to node-centred discretisation. For convection, our robust scheme was proposed by A. Dervieux (and coauthors) under the naming V4 scheme. It uses a dedicated MUSCL reconstruction with a combination of upwind and centred gradients and a dedicated slope limiter. Diffusion terms are computed using the Finite Element approximation using the gradients of the shape functions. Source terms require gradients at mesh nodes estimated using Clément’s scheme. The full discretisation is called the mixed-volume element approach.
Cooperation: G. Barreau (ONERA/DPHY), Y. Gorschka (Safran Tech), F. Pechereau (ONERA/DPHY), F. Tholin (ONERA/DPHY), C. Tarsia-Morisco (Inria/GammaO), F. Alauzet (Inria/GammaO), J. Vanharen (Inria/GammaO), A. Remigi (Safran Tech), B. Maugars (DAAA/CLEF), C. Content (DAAA/CLEF).
Error estimate
The error estimate is one root of the process. It should be based on unknowns, leading to the feature-based adaptation. Or it should require the solutions of direct and adjoint problems, leading to the goal-oriented procedure. We work on both approaches.
Cooperation: V. Golliet (ONERA/DMPE), F. Pechereau (ONERA/DPHY),
F. Alauzet (Inria/GammaO), A. Remigi (Safran Tech) and PhD students from Inria.
New applications
One of my objectives for GammaO is to promote the technology for multiphysics (reentry, arc lightning with ONERA/DPHY or turbomachinery with Safran Tech and ONERA/DAAA). Reentry is a class of flows never tested before. Hypersonic flows are characterised by strong 3D shocks, whose location depends on inflow conditions. In addition, capturing the boundary layer, especially the wall heat flux, is the main objective since heat is transferred to the wall. Our strategy is based on simplexes (triangles and tetrahedrons) in the boundary layer, which contradicts the literature for which prisms or hexahedrons must be preferred. The strength of our method is the capability to add nodes exactly where they are needed and to coarsen the mesh elsewhere. A strong mathematical environment drives everything, and the whole theoretical background explains the quality of our results.
Cooperation: V. Golliet (ONERA/DMPE), F. Pechereau (ONERA/DPHY),
F. Alauzet (Inria/GammaO), A. Remigi (Safran Tech) and PhD students from Inria.