An improved SIP scheme for numerical solutions of transonic streamfunction equations

A new improved strongly implicit procedure (SIP) is presented for solving large sets of transonic streamfunction equations with matrix of coefficients [ B ]. This algorithm has several advantages over those now in use. First, Stone's auxiliary matrix [ B ′] is non-symmetric, while in the present scheme the auxiliary matrix [ B ′] is symmetric and the matrix [ B + B ′] is positive definite and symmetric when [ B ] is a symmetric matrix. This ensures the numerical stability of the iterative algorithms. Secondly, for an appropriate choice of iterative parameter ω, the rate of convergence of the new iterative procedure should be faster than the original SIP scheme. Numerical results of the blade-to-blade flows are given with the present scheme. It is shown that the algorithm is efficient and robust.