Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-09T12:48:35.234Z Has data issue: false hasContentIssue false
  • English
  • Français

A 2D Navier-Stokes method for unsteady compressible flow calculations on moving meshes

Published online by Cambridge University Press:  04 July 2016

A. L. Gaitonde ,
D. P. Jones  and
S. P. Fiddes
A. L. Gaitonde
Affiliation:
Department of Aerospace EngineeringUniversity of Bristol Bristol, UK
D. P. Jones
Affiliation:
Department of Aerospace EngineeringUniversity of Bristol Bristol, UK
S. P. Fiddes
Affiliation:
Department of Aerospace EngineeringUniversity of Bristol Bristol, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A moving mesh method for the computation of compressible viscous flow past deforming and moving aerofoils is described. It is based on a well established time-marching finite-volume scheme, which has been widely used for steady compressible flows. An implicit real-time discretisation is used and the equations are integrated via a dual-time scheme. This involves the introduction of derivatives of a fictitious pseudo time. The solution at each real-time step involves seeking solutions which are steady-state solutions in pseudo time. This approach decouples the stability and accuracy limitations of the scheme and permits large real-time steps to be chosen. Also well-proven convergence acceleration techniques developed for steady flows such as local-time stepping, residual averaging and multigrid may be used in the pseudo-time stepping scheme without compromising real-time accuracy. A sequence of body-conforming grids and corresponding grid speeds is required, where the inner and outer boundaries of the grid move independently. The required grids and speeds are found using a transfinite interpolation technique. Applications of the method to external compressible flows are shown, including results from a parallel version of the computer program.

Type
Research Article
Information
The Aeronautical Journal , Volume 102 , Issue 1012 , February 1998 , pp. 89 - 97
Copyright
Copyright © Royal Aeronautical Society 1998 

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. Venkatakrishnan, V. and Jameson, A. Computation of unsteady transonic flows by the solution of the Euler equations, AIAA J, 1988, 26, pp 974–981.Google Scholar
2. Batina, J.T., Lee, E.M., Kleb, W.L. and Rausch, R.D. Unstructured-grid methods development for unsteady aerodynamic and aeroelastic analyses, In Transonic Unsteady Aerodynamics and Aeroelasticity, 1991.Google Scholar
3. Gaitonde, A.L. and Fiddes, S.P. A three-dimensional moving mesh system for the calculation of unsteady transonic flows, Aeronaut J, April 1995, 99, (984), pp 150–160.Google Scholar
4. 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
5. Guruswamy, G.P. Unsteady aerodynamic and aeroelastic calculations for wings using Euler equations, AIAA J, 1990, 28, pp 461–469.Google Scholar
6. Jameson, A. and Turkel, E. Implicit schemes and LU decompositions, Math Comput, 1981, 37, pp 385–397.Google Scholar
7. Jameson, A.J. Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings, AIAA Paper 91-1596, 1991.Google Scholar
8. Arnone, A., Liou, M.-S. and Povinelli, L.A. Integration of Navier-Stokes equations using dual time stepping and a multigrid method, AIAA J, 1995, 33, (6).Google Scholar
9. Gaitonde, A.L. and Jones, D.P. Parallel implementation of a dual-time moving mesh method for the 2D unsteady Navier-Stokes equations, Bristol University Aero Dept Report No 736, 1995.Google Scholar
10. 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
11. Swanson, R.C. and Turkel, E. A multistage time-stepping scheme for the Navier-Stokes equations, NASA ICASE 84-62, 1985.Google Scholar
12. Gaitonde, A.L. A dual time method for the solution of the 2D unsteady Navier-Stokes equations on structured moving meshes, Paper 95-1877, in the Proceedings of the 13th AIAA Applied Aerodynamics Conference, San Diego, 1995.Google Scholar
13. Melson, N.D., Sanetrik, M.D. and Atkins, H.L. Time-accurate Navier-Stokes calculations with multigrid acceleration, NASA CP 3224, 1993.Google Scholar
14. 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
15.AGARD Compendium of unsteady aerodynamic measurements, AGARD-R-720, 1982.Google Scholar
16. Ekaterinaris, J.A., Srinivasan, G.R. and McCroskey, W.J. Present capabilities of predicting two-dimensional dynamic stall, AGARD CP-552, 1994.Google Scholar
17. Johnston, L.J. Solution of the Reynolds-averaged Navier-Stokes equations for transonic aerofoil flows, Aeronaut J, October 1991, 95, (948), pp 253–273.Google Scholar
18. Badcock, K.J. and Gaitonde, A.L. An unfactored implicit movingmesh method for the two-dimensional unsteady N-S equations, Int J for Numer Meth in Fluids, 1996, 23, pp 607–631.Google Scholar
19. Gaitonde, A.L. A dual time method for the solution of the unsteady Euler equations, Aeronaut J, October 1994, 98, (978) pp 283–291.Google Scholar