Sails trim optimisation using CFD and RBF mesh morphing

Biancolini, Marco Evangelos; Viola, Ignazio Maria; Riotte, M.

doi:10.1016/j.compfluid.2014.01.007

Cited by 59 publications

(34 citation statements)

References 21 publications

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“…Mesh displacement based on RBF interpolation has proved to be robust for large deformations [21]. [1] compared the most common techniques, including linear and torsional springs, linear elasticity and several interpolation-based methods such as the RBF and IDW.…”

Section: Introductionmentioning

confidence: 99%

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

Gagliardi

Giannakoglou

2019

Advances in Engineering Software

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Mesh displacement based on Radial Basis Functions (RBF) interpolation is known for its ability to preserve the validity and quality of the mesh, even for large displacements, without being affected by mesh connectivity. However, in the case of large meshes, such as those used in real-world Computational Fluid Dynamics (CFD) applications, RBF interpolation, in its standard formulation, becomes excessively expensive. This paper proposes a cost reduction technique for mesh displacement based on RBF, by splitting the process into two steps. In the first step, named predictor, a data reduction algorithm that adaptively agglomerates mesh boundary nodes by reducing the RBF interpolation problem size is used. Upon completion of the first step, due to the agglomeration and the fact that the RBF interpolation is applied to the boundary nodes too, the so-displaced boundaries do not match the given displacements; thus, the position of the boundary nodes must be corrected during the second step, named corrector. The latter performs a local deformation based on RBF kernels with local support, to make the boundary conform to the known displacements of its nodes. The proposed method is accelerated by employing the Sparse Approximate Inverse preconditioner based on geometrical considerations and the Fast Multipole Method. The method and the programmed software are validated on three test cases related to the deformation of CFD meshes inside a duct and a turbine stator row as well as around a car model.

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Section: Introductionmentioning

confidence: 99%

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

Gagliardi

Giannakoglou

2019

Advances in Engineering Software

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“…RBF handles are placed arbitrarily in space (point-based), in contrast to lattice-based FFD, in which handles coincide with the vertices of polyhedra. Examples of RBF-based parameterization are presented in [7] and [8]. In [7], airfoil shapes in discrete form are controlled by RBF handles placed off the shape.…”

Section: Introductionmentioning

confidence: 99%

RBF-based morphing of B-Rep models for use in aerodynamic shape optimization

Gagliardi

Giannakoglou

2019

Advances in Engineering Software

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This paper presents a shape parameterization method based on morphing that acts directly on CAD-compatible Boundary-Representations (B-Rep), effectively integrated into aerodynamic shape optimization. The proposed technique requires the definition of a small number of "handles", which are strategically placed around or on the B-Rep shapes to be optimized. Displacement vectors associated with these handles are used as design variables in the optimization method. Using Radial Basis Functions (RBF) as an interpolation method, these displacements are transferred from the handles to the Non-Uniform Rational Basis-Splines (NURBS) control points of the B-Rep model; this approach offers the advantage that the updated surface remains in CAD format and is thus exportable to a STEP file. The proposed method combines two successive deformation steps. Each deformation is controlled by an independent set of handles, increasing the flexibility of the morphing action. A strategy for updating the CFD surface grid to the already changed B-Rep models enables the seamless inclusion of the proposed method into any optimization loop, avoiding any into-the-loop dependence on grid generation packages. The surface grid is updated by computing new nodal coordinates based on the updated NURBS parametric coordinates; these are computed according to changes in the parametric domain of trimmed surfaces by an RBF-based interpolation. The displacement of the surface nodes is then used to displace the CFD volume grid. The tool is differentiated and integrated into gradient-based optimization loops using the adjoint method to compute the gradient of the objective and constraint functions with respect to the surface nodal positions. The performance of the proposed method is assessed in four aerodynamic shape optimization problems, concerning a 2D airfoil, a duct, an aircraft model and a compressor stationary blading. An assessment of the proposed method based on parametric effectiveness, in the 2D case, is also presented.

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“…de Boer et al [15] generalized the method to unstructured grids and applied a broader class of radial basis functions. RBF-based mesh deformation is nowadays applied in a variety of research fields [25,26], has been integrated in commercial software packages [27], and is the subject of ongoing research projects [28].…”

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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Sails trim optimisation using CFD and RBF mesh morphing

Cited by 59 publications

References 21 publications

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

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

RBF-based morphing of B-Rep models for use in aerodynamic shape optimization

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

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