An interpolation tool for aerodynamic mesh deformation problems based on octree decomposition

Abstract

The necessity to modify a pre-existing computational mesh is a common requirement in many areas of computational fluid dynamics like aeroelasticity, optimization, etc. Here, we propose an approach to develop an efficient numerical mesh movement tool. The strategy relies on a three steps procedure: (i) generation of an octree decomposition of the geometry, (ii) definition of small interpolation domains, and (iii) application of local interpolation algorithms. Deformation is propagated from the moving boundaries towards the far field in a way similar to an advancing front methodology, which ensures continuity and numerical viability. The method can be applied to any type of mesh: structured, multiblock structured, unstructured and hybrid because it only uses geometric position of the mesh points, regardless of the particular mesh connectivities. The interpolation tool is based on radial basis functions. It will be showed that the method is very robust and generates a mesh with similar quality parameters as the original, it is computationally very efficient and can be easily parallelized.

A novel three-dimensional mesh deformation method based on sphere relaxation

“…The wing rotates 120 • at the final deformation step which is larger than that mentioned in Ref. [11]. The prismatic elements which construct the viscous layer rotate together with the wing, and their mesh quality is therefore preserved.…”

“…Mesh deformation methods have received much attention in recent years, for they avoid mesh regeneration which is computational burdensome and introduces interpolation errors. The methods for mesh deformation can be generally sorted into partial differential equation (PDE) methods [1,2], physical analogy techniques [3,4], algebraic methods [6][7][8][9][10][11][12] and their combinations [5]. Algebraic methods are generally more efficient than the others, and become prevailing recently.…”

“…Considerable new schemes and improvements of mesh deformation also have been developed recently. The octree decomposition was presented with the RBF interpolation to improve the deformation efficiency of large scale meshes [11]. Even an artificial neural network had been introduced with the interpolation technique to improve the efficiency of the mesh deformation method [12].…”

Aeroacoustic source term computation based on radial basis functions

“…Since then, the multiquadric approximation of scattered data has been used in geodesy, mapping, signal processing, digital terrain modeling, and hydrology . In the field of aeroelasticity, fluid‐structure interaction algorithms based on mesh‐less radial basis function (RBF) interpolation are proposed as a computational efficient coupling strategy . The coupling of nonconforming grids with focus on computational performance is of great importance in aeroelasticity …”

A two–step radial basis function-based CFD mesh displacement tool

“…Similar methods, named multilevel RBF techniques, involve successive levels of nested RBF interpolations through which, on each level, the solution from the previous coarser level is interpolated [25,26]. The mesh displacement method proposed in [27] was based on domain decomposition and local RBF interpolations resulting in a series of small problems.…”