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An Effective Numerical Method for Solving Viscous-Inviscid Interaction Problems
Marina A. Kravtsova, Vladimir B. Zametaev and Anatoly I. Ruban
Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Vol. 363, No. 1830, New developments and applications in a rapid fluid flows (May 15, 2005), pp. 1157-1168
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/30039640
Page Count: 11
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This paper presents a new numerical method to solve the equations of the asymptotic theory of separated flows. A number of measures was taken to ensure fast convergence of the iteration procedure, which is employed to treat the nonlinear terms in the governing equations. Firstly, we selected carefully the set of variables for which the nonlinear finite difference equations were formulated. Secondly, a Newton-Raphson strategy was applied to these equations. Thirdly, the calculations were facilitated by utilizing linear approximation of the boundary-layer equations when calculating the corresponding Jacobi matrix. The performance of the method is illustrated, using as an example, the problem of laminar two-dimensional boundary-layer separation in the flow of an incompressible fluid near a corner point of a rigid body contour. The solution of this problem is non-unique in a certain parameter range where two solution branches are possible.
Philosophical Transactions: Mathematical, Physical and Engineering Sciences © 2005 Royal Society