Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-11T00:32:38.530Z Has data issue: false hasContentIssue false
  • English
  • Français

High-Order Mesh Generation for Discontinuous Galerkin Methods Based on Elastic Deformation

Part of: Hyperbolic equations and systems Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  27 May 2016

Hongqiang Lu ,
Kai Cao ,
Lechao Bian  and
Yizhao Wu
Hongqiang Lu*
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Kai Cao
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Lechao Bian
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Yizhao Wu
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
*
*Corresponding author. Email:hongqiang.lu@nuaa.edu.cn (H. Q. Lu)
Get access

Abstract

In this paper, a high-order curved mesh generation method for Discontinuous Galerkin methods is introduced. First, a regular mesh is generated. Second, the solid surface is re-constructed using cubic polynomial. Third, the elastic governing equations are solved using high-order finite element method to provide a fully or partly curved grid. Numerical tests indicate that the intersection between element boundaries can be avoided by carefully defining the elasticity modulus.

Keywords

Curved mesh generationdiscontinuous Galerkin methodselastic deformationLagrangian finite element

MSC classification

Secondary: 35L67: Shocks and singularities 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 4 , August 2016 , pp. 693 - 702
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bassi, F. and Rebay, S., High-order accurate discontinuous finite element solution of the 2D Euler equations, J. Comput. Phys., 138 (1997), pp. 251–285.Google Scholar
[2]Bassi, F. and Rebay, S., A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, J. Comput. Phys., 131 (1997), pp. 267–279.CrossRefGoogle Scholar
[3]Cockburn, B., Karniadakis, G. E. and Shu, C. W., Discontinuous Galerkin Methods: Theory, Computation and Applications, Springer, Berlin, 1999.Google Scholar
[4]Gao, H. Y., Wang, Z. J. and Liu, Y., A study of curved boundary representations for 2D high order Euler solvers, J. Sci. Comput., 44 (2010), pp. 323–336.CrossRefGoogle Scholar
[5]Hindenlang, F., Gassner, G., Bolemann, T. and Munz, C. D., Unstructured high order grids and their applications in discontinuous Galerkin methods, 5th European Conference on Computational Fluid Dynamics, 14-17 June 2010, Lisbon, Portugal.Google Scholar
[6]Krivodonova, L. and Berger, M., High order accurate implementation of the solid wall boundary conditions in curved geometries, J. Comput. Phys., 211 (2006), pp. 492–512.CrossRefGoogle Scholar
[7]Lübon, C., Kessler, M., Wagner, S. and Krämer, E., High-order boundary discretization for discontinuous Galerkin codes, 25th AIAA Applied Aerodynamics Conference, 05C08 June 2006, San Francisco, California.Google Scholar
[8]Persson, P. O. and Peraire, J., Curved mesh generation and mesh refinement using Lagrangian solid mechanics, 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, 05C08 Jan 2009, Orlando, Florida.Google Scholar
[9]Tian, CH. S. and Hu, J. W., Elastic mesh deformation and its application, J. Numer. Methods Comput. Appl., 3 (2003), pp. 215–224.Google Scholar
[10]Toulorge, T. and Desmet, W., Curved boundary treatment for the discontinuous Galerkin method applied to aeroacoustic propagation, 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), 11-13 May 2009, Miami, Florida.Google Scholar