The AGE Method for Direct Numerical Simulation of Turbulent Shear Flows
Department of Mechanical Engineering,
University of Newcastle
|Computational Fluid Dynamics (CFD), that is the numerical simulation
of fluid flow, has become a significant academic research area and also
a significant industrial research and development activity over the last
two decades. An article by Parviz Moin in the Scientific American of January
1997 gives a good overview of current research and applications. Ideally,
CFD is based on the direct numerical solution of the governing nonlinear
partial differential equations of fluid flow, usually the Navier-Stokes
equations plus an equation of state or related energy equations. When the
flow is turbulent, however, direct numerical simulation (DNS) becomes very
expensive because of the wide range of timescales and spatial scales involved.
Therefore, in all commercial codes and in many research areas, new equations
are introduced to model some or all of the effects of turbulence, sometimes
with unpredictable, undesirable consequences.
The aim of the present project is to find methods of making DNS cheaper so that turbulence modelling will not be required for many cases. The work is mainly being done for simple 'canonical' shear flows so that published experimental results can be used for comparison, but the methods should be adaptable to the wide range of boundary conditions found in practical applications. The state of the project just prior to its transfer to the ANUSF (mid 1997) is described in Bisset, D.K., "The AGE method for direct numerical simulation of turbulent shear flow", to appear in Int J for Numerical Methods in Fluids. Note that AGE stands for Advected Grid Explicit, and that the fluid velocities of interest are well below sonic speed.
g91 - VPP
What are the results to date and the future of the work?
(i) The previous work on a spatially-developing two-stream mixing layer was replicated on the VPP, and then extended to higher Reynolds number. Results compare very well with published experiments, and the Reynolds number is about three times higher than that of the best previously published mixing layer simulation, which used a pseudospectral method with temporal development and was more expensive computationally. The speed of the AGE method on the
VPP allowed parametric studies of the method to be carried out, and grid refinement tests.
(ii) After brief trials with much lower velocity ratios in the mixing layer, an improved AGE method was used to simulate a turbulent planar jet of aspect ratio 20 and Reynolds number 10,000, firstly with a small co-flow and then without co-flow. The near-field of the jet is under-resolved, but results for the self-preserving region up to x = 40H (where H is the jet initial thickness) are very comparable to published experiments. To the best of my knowledge, the only published planar jet 3-D simulation used a much smaller aspect ratio and did not achieve good results.
(iii) Future work will include an investigation of the near-field of the planar jet (x < 15H) with better resolution, and will then be directed towards the simulation of wall-bounded flow (channel and/or boundary layer). Also, the emphasis will gradually shift away from pure development of simulation methods and towards investigation of the flows themselves.
What computational techniques are used?
The Advected Grid Explicit (AGE) method (developed by the investigator) is essentially a finite difference solution to the Navier Stokes equations along with mass continuity and an equation of state. It is described in Bisset, D.K. (1998), "The AGE method for direct numerical simulation of turbulent shear flow", to appear in Int J for Numerical Methods in Fluids, and certain improvements are described in the references below. Vectorization on the VPP was straightforward, except that the particular implementation of some Fortran IF statements turned out to be critical (a factor of nearly 3 in CPU time).
D. K. Bisset, The AGE method: further developments and applications, accepted for the Sixth ICFD Conference on Numerical Methods for Fluid Dynamics, Oxford, UK, 31/3/98 - 3/4/98
D. K. Bisset, and R. A. Antonia, Three-dimensional simulation of a planar turbulent jet, accepted for the Seventh European Turbulence Conference, Saint Jean Cap Ferrat, France, 30/6/98 - 3/7/98