FOURTH-ORDER ACCURATE FINITE-DIFFERENCE METHOD TO THE THREE DIMENSIONAL COMPRESSIBLE BOUNDARY LAYER EQUATIONS | ||
| International Conference on Aerospace Sciences and Aviation Technology | ||
| Article 1, Volume 3, ASAT Conference 4-6 April 1989 , CAIRO, April 1989, Pages 1-10 PDF (2.49 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/asat.1989.25852 | ||
| Author | ||
| SAMIR F. RADWAN | ||
| Assistant Professor, Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, El-Shatbey, Alexandria, EGYPT. | ||
| Abstract | ||
| This paper presents a fourth-order accurate finite-difference method for solving the full three-dimensional compressible boundary layer equations, for both subsonic and supersonic laminar flows over configurations with aerospace interest, in particular, swept wing and ellipsoid. The governing equations are written in non-orthogonal surface oriented coordinates to allow maximum flexibility in the calculations, and then are solved in similarity type trans-formed coordinates for their well advantages over the physical coordinates. The numerical scheme is an implicit finite-difference scheme with a fourth-order accuracy. It is unconditional stable, even for reversal cross-flow cases, where it is modified to satisfy the Courant-Friedrich-Levy condition. The resulting finite-difference equations form a non-linear block tridiagonal system. Newton's method is used to linearize it , and the LU-factorization method is used solve the linearized block tridiagonal system. The present method has been tested for validation. The subsonic flows over swept wing as well as a prolate spheroid are computed. Also, the case of supersonic flow, at mach number M=1.5 , past a prolate spheroid is calculated successfully. In each case, all the flow quantities such as velocity and temperature profiles, skin friction coefficients, and the boundary layer thicknesses are obtained. | ||
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