Hostname: page-component-6898cfcb55-w5hgh Total loading time: 0 Render date: 2026-11-11T11:47:20.301Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady aerodynamic calculations using three-dimensional Euler equations on unstructured dynamic grids

Published online by Cambridge University Press:  04 July 2016

K. P. Sinhamahapatr
K. P. Sinhamahapatr*
Affiliation:
Aerospace Engineering Department, Indian Institute of Technology, Kharagpur, India
Get accessRights & Permissions [Opens in a new window]

Abstract

This paper presents an algorithm to solve the three-dimensional unsteady Euler equations on unstructured tetrahedral meshes using a dynamic mesh algorithm. The driving algorithm is an upwind biased implicit second order accurate cell-centered finite volume scheme. The spatial discretisation technique involves a naturally dissipative flux-split approach that accounts for the local wave propagation characteristics of the flow and captures shock waves sharply. A continuously differentiable flux limiter has been employed to eliminate the spurious oscillations near shock waves, generally arising in calculations involving upwind biased schemes. The temporal discretisation is also second order accurate and uses a Newton linearisation for unsteady calculations. To calculate time dependent flows a dynamic mesh algorithm has been implemented in which the mesh is moved to conform to the instantaneous position of the body by modelling each edge of each cell by a spring. The paper presents a description of the solver and the grid movement algorithm along with results and comparison that assess their capabilities.

Information

Type
Research Article
Information
The Aeronautical Journal , Volume 106 , Issue 1059 , May 2002, pp. 269 - 276
Copyright
Copyright © Royal Aeronautical Society 2002 

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., Baker, T.J. and Weatherill, N.P. Calculation of inviscid transonic flow over a complete aircraft, AIAA Paper 86-0103, 1986.Google Scholar
2. Frink, N.T., Parikh, P. and Pirzadeh, S. A fast upwind solver for the Euler equations on three dimensional unstructured meshes, AIAA Paper 91-0102, 1991.Google Scholar
3. Thareja, R., Stewart, J., Hassan, O., Morgan, K. and Peraire, J. A point implicit unstructured grid dolver for the Euler and Navier-Stokes rquations, AIAA Paper 88-0036, 1988.Google Scholar
4. 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
5. Peraire, J., Vahdati, M., Morgan, K. and Zienkiewicz, O.C. Adaptive remeshing for compressible flow computations, J Comp Physics, 1987, 72, pp. 449–466.Google Scholar
6. Jameson, A. and Mavriplis, D.J. Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh, AIAA J, 1986, 24,(4), pp 611–618.Google Scholar
7. Mavriplis, D.J. Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes. AIAA J, 1988, 26, (7), pp 824–831.Google Scholar
8. Mavriplis, D.J. Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes, AIAA J. 1990, 28, (2), pp 213–221.Google Scholar
9. Batina, J.T. Unsteady Euler algorithm with unstructured dynamic mesh for complex aircraft aerodynamic analysis, AIAA J, 1991, 29, (3), pp 327–333.Google Scholar
10. Batina, J.T. Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes, AIAA J, 1991, 29, (11).pp 1836–1843.Google Scholar
11. Batina, J.T. Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing, J Aircr, 1991, 28, (6), pp 397–402.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. Jameson, A., Schmidt, W. and Turkel, E. Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time step ping schemes, AIAA Paper 81-1259, 1981.Google Scholar
14. Sinhamahapatra, K.P. and Singh, N. Two-dimensional implicit flux-split steady and unsteady Euler calculations using unstructured moving grids, Aeronaut J, March 1997, 101,(1003), pp 131–139.Google Scholar
15. Morgan, K. and Peraire, J. Finite element methods for compressible flow, Von Karman Institute for Fluid Dynamics Lecture Series 1987- 04, Computational Fluid Dynamics, Belgium. 2-6 March 1987.Google Scholar
16. Lohner, R. Finite elements in CFD: what lies ahead, Int J Numerical Methods in Engineering, 1987, 24, pp 1741–1756.Google Scholar
17. Peraire, J., Peiro, J., Formaggia, L., Morgan, K. and Zienkiewicz, O.C. Finite element Euler computations in three dimensions, Int J Numerical Methods in Engineering, 1988, 26. pp 2135–2159.Google Scholar
18. Van Leer, B. Flux-vector splitting for the Euler equations, Lecture Notes in Physics, 1982, 170, pp 507–512.Google Scholar
19. Joe, B. and Simpson, R.B. Triangular meshes for regions of complicated shape, Int J Numerical Methods in Engineering, 1986, 23. pp 751–778.Google Scholar
20. Joe, B. Delaunay versus max-min solid angle triangulations for three- dimensional mesh generation, Int J Numerical Methods in Engineering, 1991, 31, pp 987–997.Google Scholar
21. Joe, B. Three-dimensional boundary constrained triangulations. ArtificialIntelligence, Expert Systems and Symbolic Computing, 1992, pp 215–222.Google Scholar
22. Joe, B. Tetrahedral mesh generation in polyhedral regions based on polyhedron decomposition, Int J Numerical Methods in Engineering, 1994, 37, pp 93–713.Google Scholar
23. Joe, B. Construction of three-dimensional improved quality triangulations using local transformations, SIAM J Sci Comput 1995, 16, pp 1292–1307.Google Scholar
24. Preparata, F.P. and Shamos, M.I. Computational Geometry — An Introduction, Springer-Verlag, 1985.Google Scholar
25. Thomas, P.D. and Lombard, C.K. Geometric conservation law and its application to flow computations on moving grids, AIAA J, 1979, 17, (10), pp 1030–1037.Google Scholar
26. Tudeman, J. et al Transonic wind tunnel tests on an oscillating wing with external stores: Part II — the clean wing, AFFD1-TR-78-194, March 1979.Google Scholar
27. Weatherill, N.P. and Hassan, O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. Int J Numerical Methods in Engineering, 1994, 37, pp 2005–2039.Google Scholar
28. Marcum, D.L. and Weatherill, N.P. Unstructured grid generation using iterative point insertion and local reconnection, AIAA J, 1995.33, (9),pp 1619–1625.Google Scholar