Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-08T13:13:44.786Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-dimensional implicit flux split steady and unsteady Euler calculations using unstructured moving grids

Published online by Cambridge University Press:  04 July 2016

K. P. Sinhamahapatra  and
N. Singh
K. P. Sinhamahapatra
Affiliation:
Aerospace Engineering Department, Indian Institute of Technology, Kharagpur, India
N. Singh
Affiliation:
Aerospace Engineering Department, Indian Institute of Technology, Kharagpur, India
Get access Rights & Permissions [Opens in a new window]

Abstract

Two-dimensional Euler equations are solved on unstructured triangular meshes using commonly available minicomputers. The driving algorithm is an upwind biased implicit cell-centred finite volume scheme. The spatial discretisation involves a naturally dissipative flux-split approach that sharply captures Shockwaves. The grid generation method uses a type of advancing front technique which triangulates a given set of points. To demonstrate the application, the steady flow results are presented for single and two component aerofoils. The unsteady results are obtained using a dynamic mesh algorithm for an aerofoil pitching harmonically about the quarter chord. The paper presents a description of the grid generation and movement algorithm and of the Euler solver, along with results and comparison that assess their capabilities.

Information

Type
Research Article
Information
The Aeronautical Journal , Volume 101 , Issue 1003 , March 1997 , pp. 131 - 139
Copyright
Copyright © Royal Aeronautical Society 1997 

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. Jameson, A. and Mavriplis, D.J. Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh, AlAA J, 1986, 24, (4), pp 611–618.Google Scholar
2. Mavriplis, D.J. Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes, AlAA J, 1988, 26, (7), pp 824–831.Google Scholar
3. Mavriplis, D.J. Accurate Multigrid solution of the Euler equations on unstructured and adaptive meshes, AlAA J, 1990, 28, (2), pp 213–221.Google Scholar
4. Lohner, R. Finite elements in CFD: what lies ahead, Int J Num Meth Eng, 1987, 24, pp 1741–1756.Google Scholar
5. Morgan, K. and Peraire, J. Finite element methods for compressible flow, von Karman Institute for Fluid Dynamics Lecture Series 1987-04, Comp Fluid Dyn, 2-6 March 1987, Belgium.Google Scholar
6. Jameson, A., Baker, T.J. and Weatherhill, N.P. Calculation of inviscid transonic flow over a complete aircraft, AlAA Paper 86-0103, 1986.Google Scholar
7. Batina, J.T. Unsteady Euler algorithm with unstructured dynamic mesh for complex aircraft aerodynamic analysis, AlAA J, 1991, 29, (3), pp 327–333.Google Scholar
8. Batina, J.T. Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes, AlAA J, 1991, 29, (11), pp 1836–1843.Google Scholar
9. Batina, J.T. Accuracy of an unstructured-grid upwind-Euler algorithm for the ONER A M6 wing, J Aircr, 1991, 28, (6), pp 397–402.Google Scholar
10. Frink, N.T., Parikh, P. and Pirzadeh, S. A fast upwind solver for the Euler equations on three-dimensional unstructred meshes, AIAA Paper 91-0102, 1991.Google Scholar
11. Thareja, R., Stewart, J., Hassan, O., Morgan, K. and Peraire, J. A point implicit unstructured grid solver for the Euler and Navier-Stokes equations, AIAA Paper 88-0036, 1988.Google Scholar
12. Bart, T.J. and Jesperson, D.C. The design and application of upwind schemes on unstructured meshes, AIAA Paper 89-0366, 1989.Google Scholar
13. McGrory, W.D., Walters, R.W. and Lohner, R. Three-dimensional space-marching algorithm on unstructured grids, AIAA J, 1991, 29, (11), pp 1844–1849.Google Scholar
14. Watson, D.F. Computing the N-dimensional Delaunay tesselation with application to Voronoi polytopes, Comp J, 1981, 24, (2), pp 167–172.Google Scholar
15. Bowyer, A. Computing Dirichlet tesselations, Comp J, 1981, 24, (2), pp 162–167.Google Scholar
16. Tanemura, M., Ogawa, T. and Ogita, N. A new algorithm for three-dimensional Voronoi tesselation, J Comp Phys, 1983, 51, pp 191–207.Google Scholar
17. Baker, T.J. Three-dimensional mesh generation by triangulation of arbitrary point sets, AIAA-87-1124-CP, 1987, pp 255-271.Google Scholar
18. Yerry, M.A. and Shepard, M.S. Automatic three-dimensional mesh generation by the modified-octree technique, Int J Num Meth Eng, 1984, 20, pp 1965–1990.Google Scholar
19. Lo, S.H. A new mesh generation scheme for arbitrary planar domains, Int J Num Meth Eng, 1985, 21, pp 1403–1426.Google Scholar
20. Peraire, J., Vahdati, M., Morgan, K. and Zienkiewicz, O.C. Adaptive remeshing for compressible flow computations, J Comp Phys, 1987, 72, pp 449–466.Google Scholar
21. Lohner, R. and Parikh, P. Generation of three-dimensional unstructured grids by the advancing front method, AIAA Paper 88-0515, 1988.Google Scholar
22. Pirzadeh, S. Recent progress in unstructured grid generation, AIAA Paper 92-0445, 1992.Google Scholar
23. Cavendish, J.C. Automatic triangulation of arbitrary planar domains for the finite element method, Int J Num. Meth Eng, 1974, 8, pp 679–696.Google Scholar
24. Jameson, A., Schmidt, W. and Turkel, E. Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes, AIAA Paper 81 -1259, 1981.Google Scholar
25. van Leer, B. Flux-vector splitting for the Euler equations, Lecture Notes in Physics, 1982,170, pp 507–512.Google Scholar
26. Slack, D.C., Whitaker, D.L. and Walters, R.W. Time integration algorithms for the two-dimensional Euler equations on unstructured meshes, AIAA J, 1994, 32, (6), pp 1158–1166.Google Scholar
27. Thomas, J.L. and Salas, M.D. Farfield boundary conditions for transonic lifting solutions to the Euler equations, AIAA J, 1986, 24, (7), pp 1074–1080.Google Scholar
28. Batina, J.T. Unsteady Euler airfoil solutions using unstructured dynamic meshes, AIAA Paper 89-0115, 1989.Google Scholar
29. Batina, J.T. Unsteady transonic small-disturbance theory including entropy and vorticity effects, J Aircr, 1989, 26, (6), pp 531–538.Google Scholar
30. Williams, B.R. An exact test case for the plane potential flow about two adjacent lifting aerofoils, ARC R & M No 3717, 1973.Google Scholar
31. Landon, R.H. NACA 0012 oscillating and transient pitching, Compendium of Unsteady Aerodynamic Measurements, Data Set 3, AGARD-R-702, 1982.Google Scholar