Hostname: page-component-89b8bd64d-9prln Total loading time: 0 Render date: 2026-05-07T13:35:53.375Z Has data issue: false hasContentIssue false
  • English
  • Français

Quadrilateral Cell-Based Anisotropic Adaptive Solution for the Euler Equations

Published online by Cambridge University Press:  20 August 2015

H. W. Zheng ,
N. Qin ,
F. C. G. A. Nicolleau  and
C. Shu
H. W. Zheng*
Affiliation:
Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
N. Qin*
Affiliation:
Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
F. C. G. A. Nicolleau*
Affiliation:
Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
C. Shu*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
*
Email:H.W.Zheng@sheffield.ac.uk
Corresponding author. Email:n.qin@sheffield.ac.uk
Email:F.Nicolleau@Sheffield.ac.uk
Email:mpeshuc@nus.edu.sg
Get access

Abstract

An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed. The data structure, the directional refinement and coarsening, including the method for initializing the refined new cells, for the anisotropic adaptive method are described. It provides efficient high resolution of flow features, which are aligned with the original quadrilateral mesh structures. Five different cases are provided to show that it could be used to resolve the anisotropic flow features and be applied to model the complex geometry as well as to keep a relative high order of accuracy on an efficient anisotropic mesh.

Keywords

51E1265M0868U0568U20Anisotropic adaptive mesh refinementquadrilateral meshfinite volumeface-based algorithmHLLCEuler equation

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 1 , January 2011 , pp. 68 - 88
Copyright
Copyright © Global Science Press Limited 2011

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.)

Article purchase

Temporarily unavailable

References

[1]Berger, M.J. and Oliger, J.Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 1984; 53(3):484–512.Google Scholar
[2]Hornung, R. D., and Trangenstein, J. A.Adaptive mesh refinement and multilevel iteration for flow in porous media. J. Comput. Phys. 1997; 136(2):522–545.Google Scholar
[3]Popinet, S.Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 2003; 190(2):572–600.Google Scholar
[4]Liang, Q., Borthwick, A.G.L., and Stelling, G.. Simulation of Dam and Dyke-break Hydrodynamics on Dynamically Adaptive Quad-tree Grids. Int. J. for Num. Meth. in Fluids 2004; 46(2):127–162.Google Scholar
[5]Charlton, E.F., and Powell, K.G. An octree solution to conservation-laws over arbitrary regions (OSCAR). AIAA Paper 1997; 97–0198.Google Scholar
[6]Berger, M.J. and LeVeque, R.Adaptive mesh refinement for two-dimensional hyperbolic systems and the AMRCLAW software. SIAM J. Numer. Anal. 1998; 35:2298–2316.Google Scholar
[7]Zeeuw, D. De and Powell, K. G.An Adaptively Refined Cartesian Mesh Solver for the Euler Equations. J. Comput. Phys. 1993; 104(1):56–68.Google Scholar
[8]Schmidt, G. H. and Jacobs, F. J.Adaptive local grid refinement and multi-grid in numerical reservoir simulation. J. Comput. Phys. 1988; 77(1):140–165.CrossRefGoogle Scholar
[9]Wang, Z.J.A Quadtree-based adaptive Cartesian/Quad grid flow solver for Navier-Stokes equations. Computers and fluids 1998; 27(44):529–549.Google Scholar
[10]Wang, Z.J. and Srinivasan, K.An Adaptive Cartesian Grid Generation Method for ‘Dirty’ Geometry. Int. J. for Num. Meth. in Fluids 2002; 39(8):703–717.Google Scholar
[11]Wang, Z.J., Chen, R.F., Hariharan, N., Przekwas, A.J. and Grove, D. A 2N Tree Based Automated Viscous Cartesian Grid Methodology for Feature Capturing. AIAA Paper 1999; 99-3300.Google Scholar
[12]Wang, Z.J. and Chen., R.F.Anisotropic Solution-Adaptive Viscous Cartesian Grid Method for Turbulent Flow Simulation. AIAA Journal 2002; 40(10):1969–1978.Google Scholar
[13]Ham, F.E., Lien, F.S., and Strong, A.B.A Cartesian Grid Method with Transient Anisotropic Adaptation. J. Comput. Phys. 2002; 179(2):469–494.Google Scholar
[14]Keats, W.A. and Lien, F.S.Two-Dimensional Anisotropic Cartesian Mesh Adaptation for the Compressible Euler Equations. Int. J. for Num. Meth. in Fluids 2004; 46(11):1099–1125.Google Scholar
[15]Habashi, WG., Dompierre, J., Bourgault, Y., Ait-Ali-Yahia, D., Fortin, M., Vallet, MG. Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part II: Structured meshes. Int. J. for Num. Meth. in Fluids 2002; 39(8):657–673.Google Scholar
[16]Habashi, WG., Dompierre, J., Bourgault, Y., Ait-Ali-Yahia, D., Fortin, M., Vallet, MG.Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part III: Unstructured meshes. Int. J. for Num. Meth. in Fluids 2002; 39(8):675–702.Google Scholar
[17]Sun, M., and Takayama, K.Conservative smoothing on an adaptive quadrilateral grid. J. Comput. Phys. 1999; 150(1):143–180.Google Scholar
[18]Zheng, H. W., Shu, C. and Chew, Y.T.An Object-Oriented and Quadrilateral-mesh based Solution Adaptive Algorithm for Compressible Multi-fluid Flows. J. Comput. Phys. 2008; 227(14):6895–6921.Google Scholar
[19]Qin, N. and Liu, X.Flow feature aligned grid adaptation. Int. J. for Num. Meth. in Engineering 2006; 67(6):787–814.Google Scholar
[20]Toro, EF, Spruce, M., and Speares, W.Restoration of the contact surface in the HLL Riemann solver. Shock Waves 1994; 4(1):25–34.Google Scholar
[21]Toro, EF. Riemann Solvers and Numerical Methods for Fluid Dynamics (2nd edn) Springer: Berlin, 1999.Google Scholar
[22]Luo, H., Baum, J.D., and Lohner, R.A hybrid Cartesian grid and gridless method for compressible flows. J. Comput. Phys. 2006; 214(2):618–632.Google Scholar
[23]Takayama, K. and Inoue, O.Shock wave diffraction over a 90 degree sharp corner, Posters presented at 18th ISSW. Shock Waves 1991; 1(4):301–312.Google Scholar
[24]Takayama, K. and Jiang, Z.Shock wave reflection over wedges: A benchmark test for CFD and experiments. Shock Waves 1997; 7(4):191–203.Google Scholar
[25]Tang, L., and Song, H.A multiresolution finite volume scheme for two-dimensional hyperbolic conservation laws. Journal of Computational and Applied Mathematics 2008; 214(2):583–595.Google Scholar