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Linear system setup and solution
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The subsequent numerical implementation of equations (6.37) will be done in terms of the following variables normalized with VL, denoted by the overbar (). Note that U is then dimensionless, while Г and CC have units of length and 1/length, respectively.
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The linearized flow tangency conditions (6.37) constitute an N x N linear system for the Г. normalized vortex strengths when the U, C, Si terms are placed on the righthand side.
A.j = Y?(ri) ‘ no.
The Aerodynamic Influence Coefficient matrix A., and the righthand side vectors in braces are functions of the vortex lattice geometry only, and hence are known a priori.
Multiplying (6.39) through by A-1 using LU-factorization and back-substitution gives the solution vector Г. as a sum of known 6+Ni independent vectors, whose coefficients (arbitrary at this point) are the operating
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parameters Ux, Uy … SN[. When these parameters are specified, Гi is determined by summing all 6 + N vectors.
