Measuring and improving the geometric accuracy of piece-wise polynomial boundary meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:443

Article

Ruiz-Girones, Eloi¹  Sarrate, Josep²  Roca, Xevi¹ 

[1] Barcelona Supercomp Ctr BSC, Comp Applicat Sci & Engn, E-08034 Barcelona, Spain

[2] Univ Politecn Cataluna, Lab Calcul Numer LaCaN, Jordi Girona 1, E-08034 Barcelona, Spain

关键词: Curved high-order mesh;    Geometric accuracy;    Disparity measure;    Mesh optimization;    Order of convergence;    Non-interpolative meshes;   

DOI  :  10.1016/j.jcp.2021.110500

来源: Elsevier

【 摘 要 】

We present a new disparity functional to measure and improve the geometric accuracy of a curved high-order mesh that approximates a target geometry model. We have devised the disparity to account for compound models, be independent of the entity parameterization, and allow trimmed entities. The disparity depends on the physical mesh and the auxiliary parametric meshes. Since it is two times differentiable on all these variables, we can minimize it with a second-order method. Its minimization with the parametric meshes as design variables measures the geometric accuracy of a given mesh. Furthermore, the minimization with both the physical and parametric meshes as design variables improves the geometric accuracy of an initial mesh. We have numerical evidence that the obtained meshes converge to the target geometry (unitary normal) algebraically, in terms of the element size, with order 2p (2p -1, respectively), where p is the polynomial degree of the mesh. Although we obtain meshes with non-interpolative boundary nodes, we propose a post-process to enforce, if required by the application, meshes with interpolative boundary nodes and featuring the same order of geometric accuracy. In conclusion, we can obtain super-convergent orders, at least for sufficiently smooth parametric curve (surface) entities, for meshes of polynomial degrees up to 4 (3, respectively). In perspective, this superconvergence might enable using a lower polynomial degree to approximate the geometry than to approximate the solution without hampering the required geometric accuracy for high-order analysis. (c) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

【 授权许可】

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