Efficient iterative methods applied to the solution of transonic flows (Q1913718)

We investigate the use of an inexact Newton's method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. We apply Newton's method using an exact analytic determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested: a block \(s\)-step version of the classical Orthomin\((k)\) algorithm called orthogonal \(s\)-step Orthomin (OSOmin), and the well-known GMRES method.