An Improved Time Marching Method for Turbomachinery Flow Calculation

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Abstract
Time marching solutions of the Euler equations are now very widely used for the calculation of flow through turbomachinery blade rows. All methods suffer from the disadvantages of shock smearing, lack of entropy conservation, and comparatively long run times. A new method is described which reduces all these problems. The method is based on the author’s opposed difference scheme, but this is applied to a new type of grid consisting of quadrilateral elements which do not overlap and have nodes only at their corners. The use of a nonoverlapping grid reduces finite differencing errors and gives complete freedom to vary the size of the elements. Both these factors help to improve entropy conservation. Considerable savings in run time (by a factor of about 3) are obtained by using a simple multigrid method whereby the solution is advanced simultaneously on a course and on a fine grid. The resulting method is simpler, faster, and more accurate than its predecessor.

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