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Numerical solution of transonic full‐potential‐equivalent equations in von Mises co‐ordinates
Author(s) -
An C.F.,
Barron R. M.
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650150806
Subject(s) - transonic , mathematics , ordinate , shock (circulatory) , mathematical analysis , supercritical flow , aerodynamics , flow (mathematics) , geometry , mechanics , physics , medicine
In this paper a new approach to calculate transonic flows is developed. A set of full‐potential‐equivalent equations in the von Mises co‐ordinate system is formulated under the irrotationality and isentropic assumptions. The emphasis is placed on supercritical flow, in which the treatment of embedded shock waves is crucial to get convergent solutions. Shock jump conditions are employed and shock point operators (SPOs) are constructed in the body‐fitting streamline co‐ordinate system. SPOs and a type‐dependent difference scheme are applied to solve the ‘main’ equation for the ‘main’ variable, the streamline ordinate y . A number of ‘secondary’ equations are deduced for the corresponding ‘secondary’ variables. An optimal combination for the ‘secondary’ variable, its equation and related difference scheme is selected to be the generalized density R , its linear equation and the Crank‐Nicolson scheme. Numerical results show that the present approach gives good agreement with experimental data and other computational work for NACA0012 and biconvex aerofoils in both subcritical and supercritical ranges.