Abstract
A 3-D curved mesh generator is prescribed for converting linear elements to quadratic elements required by high-order methods, which is based on the reconstruction of Cubic Bézier surfaces. Successive curved mesh refinement is also supported by inquiring the middle nodes of the edges and faces of the reconstructed quadratic elements via the Cubic Bézier surface method. Numerical test cases are shown to demonstrate the capability of both mesh curving and refinement around three-dimensional geometries.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Li, S.-J.: A parallel discontinuous Galerkin method with physical orthogonal basis on curved elements. Proc. Eng. 61, 144–151 (2013)
Li, S.-J., Wang, Z.J., Ju, L., Luo, L.-S.: Explicit large time stepping with a second-order exponential time integrator scheme for unsteady and steady flows. AIAA Paper, 2017–0753
Li, S.-J., Wang, Z.J., Ju, L., Luo, L.-S.: Fast time integration of Navier-Stokes equations with an exponential-integrator scheme. AIAA Paper, 2018–0369
Li, S.-J., Luo, L.-S., Wang, Z.J., Ju, L.: An exponential time-integrator scheme for steady and unsteady inviscid flows. J. Comput. Phys. 365, 206–225 (2018)
Li, S.-J.: Efficient p-multigrid method based on an exponential time discretization for compressible steady flows. arXiv:1807.0115
Li, S.-J., Ju, L.: Exponential time-marching method for the unsteady Navier-Stokes equations. AIAA Paper, 2019-0907
Bassi, F., Rebay, S.: High-order accurate discontinuous finite element solution of the 2D Euler equations. J. Comput. Phys. 138(2), 251–285 (1997)
Krivodonova, L., Berger, M.: High-order accurate implementation of solid wall boundary conditions in curved geometries. J. Comput. Phys. 211(2), 251–285 (2006)
Yamaguchi, F.: Curves and Surfaces in Computer Aided Geometric Design. Springer, Heidelberg (1988)
Vlachos, A., Peters, J., Boyd, C., et al.: Curved PN triangles. In: Proceedings of the 2001 Symposium on Interactive 3D Graphics. ACM Press, New York (2001)
Brodersen, O., Stürmer, A.: Drag prediction of engine-airframe interference effects using unstructured Navier-Stokes calculations. AIAA Paper, 2001–2414
Shepard, D.: A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings of the 1968 ACM National Conference, pp. 517–524 (1968)
Zhang, S.: Successive subdivisions of tetrahedra and multigrid methods on tetrahedral meshes. Houston J. Math. 21, 541–556 (1995)
Hindenlang, F., Bolemann,T., Munz, C.-D.: Mesh curving techniques for high order discontinuous Galerkin simulations. In: IDIHOM: Industrialization of High-Order Methods-A Top-Down Approach, pp. 133–152. Springer, Berlin (2015)
Ims, J., Duan, Z., Wang, Z.J.: meshCurve: an automated low-order to high-order mesh generator. AIAA Paper, 2015–2293
Jiao, X., Wang, D.: Reconstructing high-order surfaces for meshing. Eng. Comput. 28(4), 361–373 (2012)
Acknowledgements
This work is funded by the National Natural Science Foundation of China (NSFC) under the Grant U1530401. The author thanks Dr. Hang Si of WIAS, Germany, for the discussion and collaboration in a broad sense of computational geometry. SJL would further like to thank the reviewers for their helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Li, SJ. (2019). Mesh Curving and Refinement Based on Cubic Bézier Surface for High-Order Discontinuous Galerkin Methods. In: Garanzha, V., Kamenski, L., Si, H. (eds) Numerical Geometry, Grid Generation and Scientific Computing. Lecture Notes in Computational Science and Engineering, vol 131. Springer, Cham. https://doi.org/10.1007/978-3-030-23436-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-23436-2_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-23435-5
Online ISBN: 978-3-030-23436-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)