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Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra

Sachdev, PL and Lobo, M (1982) Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra. In: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, 380 (1778). pp. 77-97.

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Abstract

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, 'sharp-shock solutions' have also been obtained by the implementation of a quadratic iterative scheme with the 'artificial viscosity solution' as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to The Royal Society
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 30 Sep 2009 09:29
Last Modified: 19 Sep 2010 05:46
URI: http://eprints.iisc.ernet.in/id/eprint/23512

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