Finite transformation rigid motion mesh morpher; A grid deformation approach

• Published in: International journal for numerical methods in fluids Vol. 93; no. 3; pp. 874 - 891
• Main Authors: Liatsikouras, Athanasios G., Fougeron, Gabriel, Eleftheriou, George S., Pierrot, Guillaume
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01-03-2021
• Subjects: Adaptation; Aerodynamics; Algorithms; as‐rigid‐as‐possible; Boundaries; Computational fluid dynamics; Computational grids; Computer applications; Computer graphics; Deformation; Elastic deformation; Finite element method; Fluid dynamics; grid displacement; Hydrodynamics; mesh anisotropy; mesh‐free/mesh‐less; Movement; Nodes; nonlinear constraint; Optimization; rigid motion; Rigidity; Shape optimization; stencils; Viscous flow
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4912

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 mesh‐free grid deformation approach, appropriate for shape optimization is presented, which is able to handle mesh anisotropies (incl. boundary layers), large and extreme deformation fields very efficiently and with an affordable cost, in comparison to the cost of solving the flow equations, by preserving a good grid quality during deformation. It can handle any kind of mesh, since it is a mesh‐free method which means that the mesh connectivity is not required to deform the mesh.