On the 3-D inverse potential target pressure problem. Part 2. Numerical aspects and application to duct design

Abstract

A potential function/stream function formulation is introduced for the solution of the fully 3-D inverse potential ‘target pressure’ problem. In the companion paper (Part 1) it is seen that the general 3-D inverse problem is ill-posed but accepts as a particular solution elementary streamtubes with orthogonal cross-section. Under this simplification, a novel set of flow equations was derived and discussed. The purpose of the present paper is to present the computational techniques used for the numerical integration of the flow and geometry equations proposed in Part 1. The governing flow equations are discretized with centred finite difference schemes on a staggered grid and solved in their linearized form using the preconditioned GMRES algorithm. The geometry equations which form a set of first-order o.d.e.s are integrated numerically using a second-order-accurate space marching scheme. The resulting computational algorithm is applied to a double turning duct and a 3-D converging-diverging nozzle ‘reproduction’ test case.