High-order curvilinear meshing using a thermo-elastic analogy

Moxey, David; Ekelschot, Dirk; Keskin, Ümit; Sherwin, Spencer J.; Peiró, Joaquim

doi:10.1016/j.cad.2015.09.007

Cited by 61 publications

(37 citation statements)

References 20 publications

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“…For complex three-dimensional geometries, the generation of high-order curved meshes along solid surfaces is a challenging topic [51,52,53,54,55]. Approaches for generating unstructured high-order meshes, extending coarse linear grids to incorporate high-order curvature, are a relatively new development [52,56,57].…”

Section: High-order Mesh Generationmentioning

confidence: 99%

Spectral/hp element methods: Recent developments, applications, and perspectives

Cantwell

Monteserin

et al. 2018

J Hydrodyn

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Abstract:The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a 0 -C continuous expansion. Computationally and theoretically, by increasing the polynomial order p , high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.

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Section: High-order Mesh Generationmentioning

confidence: 99%

Spectral/hp element methods: Recent developments, applications, and perspectives

Cantwell

Monteserin

et al. 2018

J Hydrodyn

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“…Generating high-order mesh from the baseline linear mesh is a hot topic in the CFD community. Many authors have successfully proposed different algorithms to ensure the accuracy and robustness, [54][55][56][57][58][59][60] but challenges still remain to guarantee high quality for arbitrary complex geometry. If high-order unstructured solver like discontinuous Galerkin is used in the AMR simulation, suitable high-order mesh generation algorithm should be carefully used to ensure the robustness.…”

Section: Generation Algorithm Of the High-order Meshmentioning

confidence: 99%

A high‐order element based adaptive mesh refinement strategy for three‐dimensional unstructured grid

Gou

Yuan

Chen

2017

Numerical Methods in Fluids

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Summary Adaptive mesh refinement (AMR) shows attractive properties in automatically refining the flow region of interest, and with AMR, better prediction can be obtained with much less labor work and cost compared to manually remeshing or the global mesh refinement. Cartesian AMR is well established; however, AMR on hybrid unstructured mesh, which is heavily used in the high‐Reynolds number flow simulation, is less matured and existing methods may result in degraded mesh quality, which mostly happens in the boundary layer or near the sharp geometric features. User intervention or additional constraints, such as freezing all boundary layer elements or refining the whole boundary layer, are required to assist the refinement process. In this work, a novel AMR strategy is developed to handle existing difficulties. In the new method, high‐order unstructured elements are first generated based on the baseline mesh; then the refinement is conducted in the parametric space; at last, the mesh suitable for the solver is output. Generating refined elements in the parametric space with high‐order elements is the key of this method and this helps to guarantee both the accuracy and robustness. With the current method, 3‐dimensional hybrid unstructured mesh of huge size and complex geometry can be automatically refined, without user intervention nor additional constraints. With test cases including the 2‐dimensional airfoil and 3‐dimensional full aircraft, the current AMR method proves to be accurate, simple, and robust.

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“…1,2 The L-E schemes rely on properties of visco-elastic solids. Meshes are treated as a collection of deformable solids, such as pliable rubber.…”

Section: Introductionmentioning

confidence: 99%

High-Order Mesh Curving Using WCN Mesh Optimization

Karman

Erwin²,

Glasby³

et al. 2016

46th AIAA Fluid Dynamics Conference

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Linear hybrid unstructured meshes are elevated to high-order meshes using a mesh smoothing scheme. The linear meshes are first elevated to highorder by introducing new edge, face and internal nodes. Then the high-order elements are subdivided into a collection of linear sub-elements. Node perturbation vectors are computed for the new surface nodes. Employing a mesh smoothing/optimization method on the linear sub-elements curves the high-order mesh. The mesh smoothing method is an extension of an optimization-based node perturbation technique that uses a cost function to enforce desired element shapes. Details of the mesh elevation and smoothing process are described. Several three-dimensional examples are included that demonstrate the effectiveness of the method to produce high quality highorder meshes.Nomenclature [A] = Jacobian matrix for condition number C, C min = Cost function, minimum cost function WCN = Weighted condition number J = Magnitude of Jacobian matrix ! p n = Perturbation vector for node n ! s n = Sensitivity vector for node n [W] = Weight matrix for weighted condition number X, Y, Z = Cartesian physical coordinates Ω = Relaxation parameter

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High-order curvilinear meshing using a thermo-elastic analogy

Cited by 61 publications

References 20 publications

Spectral/hp element methods: Recent developments, applications, and perspectives

Spectral/hp element methods: Recent developments, applications, and perspectives

A high‐order element based adaptive mesh refinement strategy for three‐dimensional unstructured grid

High-Order Mesh Curving Using WCN Mesh Optimization

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