Samtaney, Ravi and Pullin, D. I. (1996) On initial-value and self-similar solutions of the compressible Euler equations. Physics of Fluids, 8 (10). pp. 2650-2655. ISSN 1070-6631 http://resolver.caltech.edu/CaltechAUTHORS:SAMpof96
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We examine numerically the issue of convergence for initial-value solutions and similarity solutions of the compressible Euler equations in two dimensions in the presence of vortex sheets (slip lines). We consider the problem of a normal shock wave impacting an inclined density discontinuity in the presence of a solid boundary. Two solution techniques are examined: the first solves the Euler equations by a Godunov method as an initial-value problem and the second as a boundary value problem, after invoking self-similarity. Our results indicate nonconvergence of the initial-value calculation at fixed time, with increasing spatial-temporal resolution. The similarity solution appears to converge to the weak 'zero-temperature' solution of the Euler equations in the presence of the slip line. Some speculations on the geometric character of solutions of the initial-value problem are presented.
|Additional Information:||©1996 American Institute of Physics. Received 9 January 1996; accepted 20 May 1996. This work was supported in part by AFOSR Grant No. F49620-93-1-0338. Useful discussions with P. Dimotakis, T. Hou, D. I. Meiron and J. Quirk are gratefully acknowledged. This research was performed in part using the CSCC parallel computer system operated by Caltech on behalf of the Concurrent Supercomputing Consortium.|
|Subject Keywords:||COMPRESSIBLE FLOW; VORTEX FLOW; SHOCK WAVES; BOUNDARY–VALUE PROBLEMS; NUMERICAL SOLUTION; EULER EQUATIONS; SELF–SIMILIAR STATES; GAS DYNAMICS; FLUID–FLUID INTERFACES|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||21 Jun 2006|
|Last Modified:||26 Dec 2012 08:55|
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