Finite transformation rigid motion mesh morpher; A grid deformation approach

Abstract

Summary In any shape optimization framework and specifically in the context of computational fluid dynamics, a robust and reliable grid deformation tool is necessary to undertake the adaptation of the computational mesh to the updated boundaries at each optimization cycle. Grid deformation has its share of challenges, namely, to maintain high mesh quality (avoid distorted elements and tangles) even when dealing with extreme deformations. In this work a novel grid deformation algorithm, the finite transformation rigid motion mesh morpher (FT‐R3M) is proposed. FT‐R3M is essentially a mesh‐free grid deformation approach, since it does not require any inertial quantities and it gracefully propagates the movement of the boundaries (surface mesh) to the internal nodes of the mesh (volume mesh), by keeping the motion of its parts (referred to as stencils) as‐rigid‐as‐possible. It is an optimization‐based method, which means that the interior nodes of the computational mesh are displaced to minimize a distortion metric related to the elastic deformation energy, by favoring rigidity in critical directions, thus being able to handle mesh anisotropies very efficiently. Results are presented for three test cases; a rotated airfoil with a mesh appropriate for viscous flow; a simulation of a low Reynolds duct case; a beam.

A coupled CAD‐free parameterization‐morphing method for adjoint‐based shape optimization

“…The finite transformation rigid motion mesh morpher (FT‐R3M) 44,45 has been proven capable of undergoing extreme deformations, whilst ensuring a good resulting grid quality. FT‐R3M is a minimization‐based grid displacement technique, in which the target is to minimize an objective function related to the deformation energy between the initial and the final mesh.…”

“…FT‐R3M is a minimization‐based grid displacement technique, in which the target is to minimize an objective function related to the deformation energy between the initial and the final mesh. The FT‐R3M is an in‐house grid displacement tool of ESI group developed in References 44,45. FT‐R3M is a mesh‐less method and tool which gracefully propagates the movement of the boundaries (surface changes) to the internal nodes of the volume mesh.…”

“…Furthermore, $$$ {w}_s $$$ is a scalar weight per stencil that stresses the importance of some stencils as higher than some others' and $$$ {\mu}_{s, ij} $$$ a weight per edge that accounts for mesh anisotropy. It has been proven in References 44,45 that, FT‐R3M is very robust and can handle mesh anisotropies and rotations very efficiently. In this article, due to the fact that FT‐R3M is developed from the same authors, it is also used to support the SHT.…”

“…In this article, due to the fact that FT‐R3M is developed from the same authors, it is also used to support the SHT. For more details regarding the FT‐R3M as stand‐alone tool can be found in References 44,45.…”