Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T07:22:57.851Z Has data issue: false hasContentIssue false
  • English
  • Français

A dual-time method for the solution of theunsteady Euler equations

Published online by Cambridge University Press:  04 July 2016

A. L. Gaitonde
A. L. Gaitonde*
Affiliation:
Department of Aerospace EngineeringUniversity of BristolBristol, United Kingdom
Get access Rights & Permissions [Opens in a new window]

Abstract

A “dual-time” method for solving the three-dimensional Euler equations describing the compressible flow about wings undergoing arbitrary motions and deformations is presented. A finite-volume formulation is chosen where the volumes distort as the wing moves or deforms. Independent motion of the inner and outer boundaries of the grid is permitted with a sequence of grids generated using transfinite interpolation.

An implicit real-time discretisation is used, and the equations are integrated in a fictitious pseudo time. This approach allows the real-time step to be chosen on the basis of accuracy rather than stability. It also permits the acceleration techniques commonly used to speed up steady flow calculations to be used when marching in pseudo time, without compromising real-time accuracy. A two-dimensional version of the method has also been developed and results for both two and three-dimensional transonic flows are presented and compared with experimental data where available.

Type
Research Article
Information
The Aeronautical Journal , Volume 98 , Issue 978 , October 1994 , pp. 283 - 291
Copyright
Copyright © Royal Aeronautical Society 1994 

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. Gaitonde, A.L. and Fiddes, S.P. A three-dimensional moving mesh system for the calculation of unsteady transonic flows, Paper 13 in the proceedings of the European Forum for Recent Developments and Applications in Aeronautical CFD, Bristol, 1993.Google Scholar
2. Badcock, K.J. Computation of Turbulent Pitching Aerofoil Flows, University of Glasgow, Aero report 9322, 1993.Google Scholar
3. Brenneis, A. and Eberle, A. Evaluation of an unsteady implicit Euler code against two and three-dimensional standard configurations, Paper 10 in AGARD CP-507, 1991.Google Scholar
4. Guruswamy, G.P. Unsteady aerodynamic and aeroelastic calculations for wings using Euler equations, AIAA J, 1990, 28, pp 461–469.Google Scholar
5. Jameson, A. and TURKEL, E. Implicit schemes and LU decompositions, Math Comput, 1981, 37, pp 385–397.Google Scholar
6. Jameson, A.J. Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings, AIAA Paper 91–1596 (1991).Google Scholar
7. Gaitonde, A. L. and Fiddes, S.P. The Generation of Three - Dimensional Moving Grids Using Transfinite Interpolation, Bristol University Aero Eng Dept Report No 477, 1993.Google Scholar
8. Jameson, A.J., Schmidt, W. and Turkel, E. Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes, AIAA Paper 81–1259, 1981.Google Scholar
9. 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
10. AGARD Compendium of Unsteady Aerodynamic Measurements AGARD-R-720, 1982.Google Scholar
11. Mabey, D.G. Welsh, B.L. and Pyne, C.R. Measurements of Steady and Oscillatory Pressures on a Rectangular Wing, RAE Technical Report TR86040, 1986.Google Scholar
12. AGARD Compendium of Unsteady Aerodynamic Measurements AGARD-R-720, Addendum 1, 1982.Google Scholar