A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

doi:10.1007/s42967-021-00163-0

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (1): 315-342.doi: 10.1007/s42967-021-00163-0

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A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

Xucheng Meng^1,2, Yaguang Gu³, Guanghui Hu^4,5,6

1 Research Center for Mathematics, Beijing Normal University at Zhuhai, Zhuhai 519087, Guangdong, China;
2 Division of Science and Technology, BNU-HKBU United International College, Zhuhai 519087, Guangdong, China;
3 School of Mathematical Sciences, Ocean University of China, Qingdao 266100, Shandong, China;
4 Department of Mathematics, University of Macau, Macao S. A. R., China;
5 Zhuhai UM Science and Technology Research Institute, Zhuhai 519000, Guangdong, China;
6 Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Dynamics and Engineering Applications, University of Macau, Macao S. A. R., China

Received:2021-03-11 Revised:2021-07-22 Online:2023-03-20 Published:2023-03-08
Contact: Guanghui Hu,E-mail:huyangemei@gmail.com E-mail:huyangemei@gmail.com
Supported by:
The research of Xucheng Meng is partially supported by the Scientific Research Fund of Beijing Normal University (Grant No. 28704-111032105), and the Start-up Research Fund from BNU-HKBU United International College (Grant No. R72021112). The research of Guanghui Hu was partially supported by the FDCT of the Macao S. A. R. (0082/2020/A2), the National Natural Science Foundation of China (Grant Nos. 11922120, 11871489), the Multi-Year Research Grant (2019-00154-FST) of University of Macau, and a Grant from Department of Science and Technology of Guangdong Province (2020B1212030001).

Abstract

Abstract: In Li and Ren (Int. J. Numer. Methods Fluids 70: 742–763, 2012), a high-order k-exact WENO finite volume scheme based on secondary reconstructions was proposed to solve the two-dimensional time-dependent Euler equations in a polygonal domain, in which the high-order numerical accuracy and the oscillations-free property can be achieved. In this paper, the method is extended to solve steady state problems imposed in a curved physical domain. The numerical framework consists of a Newton type finite volume method to linearize the nonlinear governing equations, and a geometrical multigrid method to solve the derived linear system. To achieve high-order non-oscillatory numerical solutions, the classical k-exact reconstruction with k = 3 and the efficient secondary reconstructions are used to perform the WENO reconstruction for the conservative variables. The non-uniform rational B-splines (NURBS) curve is used to provide an exact or a high-order representation of the curved wall boundary. Furthermore, an enlarged reconstruction patch is constructed for every element of mesh to significantly improve the convergence to steady state. A variety of numerical examples are presented to show the effectiveness and robustness of the proposed method.

Key words: Steady Euler equations, Curved boundary, NURBS-enhanced finite volume method, WENO reconstruction, Secondary reconstruction

CLC Number:

65M22
65M50

Xucheng Meng, Yaguang Gu, Guanghui Hu. A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries[J]. Communications on Applied Mathematics and Computation, 2023, 5(1): 315-342.

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A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

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