Improved Point Selection Method for Hybrid-Unstructured Mesh Deformation Using Radial Basis Functions

Wang, Gang; Mian, Haris Hameed; Ye, Zhengyin; Lee, Jen-Der

doi:10.2514/1.j053304

Cited by 71 publications

(29 citation statements)

References 21 publications

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“…Although this leads to significant speed-up, it also introduces an error at the unused boundary nodes, hence necessitating an additional correction step [31] (e.g., by means of Delaunay graph mapping [32]). Other recent developments in this direction can be found in [33,34,35].…”

Section: Introductionmentioning

confidence: 99%

Efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method

Coulier

Darve

2016

Computer Methods in Applied Mechanics and Engineering

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Radial basis function interpolation is often employed in mesh deformation algorithms for unstructured meshes, for example in fluid-structure interaction or design optimization problems. This is known to be a robust methodology that results in high quality deformed meshes. The applicability of this method to large problems is currently hampered by its prohibitive computational cost, however, which is caused by the need to solve a dense system of equations. The computation time grows as O(N 3 b) if a direct solver is employed for the solution (where N b denotes the number of boundary nodes in the mesh), while alternative iterative solvers often suffer from an unfavorable convergence behavior. In this paper, we present the inverse fast multipole method as a novel fast approximate direct solver with a computational cost scaling as O(N b). The linear complexity is achieved by transforming the dense system into an extended sparse system, along with the compression of certain matrix blocks into low-rank factorizations. The solver is inexact, although the error can be controlled and made as small as needed; a low accuracy solver can hence be used as an efficient preconditioner in an iterative scheme. Numerical benchmarks are presented, demonstrating that the proposed approach enhances the computational efficiency of mesh deformation algorithms based on radial basis function interpolation significantly, without jeopardizing their robustness and quality.

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Section: Introductionmentioning

confidence: 99%

Efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method

Coulier

Darve

2016

Computer Methods in Applied Mechanics and Engineering

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“…The size of the linear system to be solved is directly related to the number of the moving surface mesh points. To accelerate the computation, data reduction algorithms were proposed by Rendall and Allen [11,12,13], Sheng and Allen [16] and Wang et al [17] to limit the RBF interpolation on a coarsened subset of surface mesh. To decrease the error on the surface points, they applied a greedy algorithm to select the optimum reduced set of surface mesh.…”

Section: Introductionmentioning

confidence: 99%

Deformable Overset Grid for Multibody Unsteady Flow Simulation

et al. 2016

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A deformable overset grid method is proposed to simulate the unsteady aerodynamic problems with multiple flexible moving bodies. This method uses an unstructured overset grid coupled with local mesh deformation to achieve both robustness and efficiency. The overset grid hierarchically organizes the sub-grids into CLUSTERs and LAYERs, allowing for overlapping/embedding of different type meshes, in which the mesh quality and resolution can be independently controlled. At each time step, mesh deformation is locally applied to the sub-grids associated with deforming bodies by an improved Delaunay graph mapping method that uses a very coarse Delaunay mesh as the background graph. The graph is moved and deformed by the spring analogy method according to the specified motion and then the computational meshes are relocated by a simple one-to-one mapping. An efficient implicit hole-cutting and inter-grid boundary definition procedure is implemented fully automatically for both cell-centered and cell-vertex schemes based on the wall distance and an alternative digital tree (ADT) data search algorithm. This method is successfully applied to several complex multi-body unsteady aerodynamic simulations and the results demonstrate the robustness and efficiency of the proposed method for complex unsteady flow problems, particularly for those involve simultaneous large relative motion and self-deformation. --------------------

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“…Some techniques are dedicated for structured grids [10,11] while others are developed for unstructured mesh topology [12 -14]. Recently, mesh movement algorithm based on radial basis function (RBF) interpolation [15,16] has gained lot of interest. This technique has several advantages; it is independent of the type of mesh and the nature of the flow solver, the method does not require any mesh connectivity information, the method is computationally efficient and can be readily parallelized.…”

Section: Introductionmentioning

confidence: 99%

“…(7)), is solved for the complete domain it will make the method computationally expensive for very large degrees of freedom problems. Therefore, REF interpolation has been combined with a data reduction "double edged" greedy algorithm [16]. Before starting the greedy cycle a list of surface points is selected as an initial guess.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of aberrant aerodynamic behavior of wrap-around fins in collation with planar fins

Umar¹,

Mian²

2015

2015 12th International Bhurban Conference on Applied Sciences and Technology (IBCAST)

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The anomalistic aerodynamic behavior of wrap around fins has kept the researchers engrossed in devising new design methods and analysis techniques. Rolling moment at zero incidence angle, induced forces and moments due to fin curvature, roll reversal phenomenon, static side moment and Magnus side moment are the main aggravations that make their aerodynamics more complex when compared with the planar fins. The present research effort provides a deep insight and explanation for this uncertain aerodynamics associated with wrap-around fins. At first, simulations of flow around isolated planar fin and curved fin has been performed to identify the effect of curvature. The results indicate a pressure loading for the curved fin at zero incidence angle, which was more confined towards the leading edge. Both curved and flat fins showed symmetric pressure distribution about mid chord on top and bottom surfaces. As a result, no side force was observed for isolated fins. Pressure loadings have distinct divisions for both the planar and curved fins that are similar in appearance to Mach lines. Subsequently, the effect of wall and the support hinges have been studied for wrap-around fins. Due to wall boundary the pressure distribution becomes asymmetric, which originates a side force. The presence of the support hinges creates shocks patterns at the bottom surface and generates unbalanced pressure loading. The predicted aerodynamic load for the wrap around fins is then used to perform static computational aeroelastic analysis to obtain true structural deformations. The results highlights the fact that the uneven structural displacements give rise to out of the plane forces that effects the aerodynamics and flight performance of systems with wrap around fins.

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Improved Point Selection Method for Hybrid-Unstructured Mesh Deformation Using Radial Basis Functions

Cited by 71 publications

References 21 publications

Efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method

Efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method

Deformable Overset Grid for Multibody Unsteady Flow Simulation

Numerical investigation of aberrant aerodynamic behavior of wrap-around fins in collation with planar fins

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