Numerical simulation of axisymmetric converging flows using the stream tube method and a Trust Region optimization algorithm

This paper examines the numerical simulation of axisymmetric converging flows. The analysis is performed by means of the stream tube method which permits computation of the unknowns in a transformed domain where the streamlines are parallel and straight. The relevant non-linear equations are solved numerically by using a new algorithm based on a Trust Region technique which is efficient for non-convex optimization problems. In this work, the authors present the main features of the stream tube method and the theoretical elements of the Trust Region algorithm. Converging flows are considered as illustrative examples, showing that the new algorithm is more robust compared to the Newton-Raphson method.