NATURAL FORMULATION OF THE RANDOM CHOICE METHOD FOR TWO–DIMENSIONAL INERT HIGH–SPEED FLOW FIELDS
✍ Scribed by A. S. DAWES
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 584 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0271-2091
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✦ Synopsis
The random choice method has now been shown to be successfully extendible from the original one-dimensional unsteady formulation to inert high-speed flow fields which are steady and two-dimensional using Cartesian, axisymmetric and Lagrangian formulations. This paper deals with the description of a new implementation of the random choice method formulated for natural co-ordinates based on streamlines and normals. Comparisons between theoretical and computed results for several different physical configurations are presented. KEY WORDS Euler equations; hyperbolic; initial boundary value problem; natural co-ordinate system; random choice method; Rlernann problem
MTRODUCIION
The random choice method (RCM) is based on an existence proof by Glimm' for solutions to systems of non-linear hyperbolic, one-dimensional, unsteady equations. Chorin2 developed it into a practical numerical method which was subsequently improved by C ~l e l l a , ~ Gottlieb? Sod' and Toro6 to name but a few. The equations for steady, two-dimensional, supersonic flow fields are hyperbolic and are similar to the one-dimensional equations. This property has been used to develop the RCM for Cartesian and axisymmetric co-ordinate systems7 l o and for the Lagrangian co-ordinate system.' In recent years the RCM has lost favour to other numerical schemes, for example schemes that incorporate the total variational diminishing (TVD) This is because the RCM cannot be successhlly applied to multidimensional problem^.'^ However, there are two strong reasons for using the method which others struggle to match. Firstly, discontinuities, as shocks or contact surfaces, suffer tiom no numerical diffusion or oscillations. Secondly, shock waves are predicted with infinite resolution.
The Euler equations are presented for the natural co-ordinate system based on streamlines and normals. This choice of co-ordinate space has the advantage of capturing physical boundaries exactly. The RCM is then described in detail. Finally, a comparison of computed and theoretical results for several configurations is presented.