FOURTH-ORDER ACCURATE FINITE-DIFFERENCE METHOD TO THE THREE DIMENSIONAL COMPRESSIBLE BOUNDARY LAYER EQUATIONS

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.