CFD code convergence diagnostics and acceleration using the Recursive Projection Method

Mihai Dorobantu, Kurt Lust, Alexander Khibnik, and Joakim Moller

United Technologies Research Center
411 Silver Lane, MS 129-15
East Hartford, CT - 06108


Under the general paradigm of the Recursive Projection Method (RPM) developed by H. Keller as a stabilization method for stabilizing unstable nonlinear oscillations, we have created a framework for analyzing and diagnosing convergence problems encountered in flow simulations. The RPM framework contains three independent modules: a procedure to identify leading eigenvalues of the iteration operator, a nonlinear Newton-type solver for small systems, and the interface to the specific CFD code used. In this talk we present a series of applications that illustrate how a combination of eigenvalue solvers and nonlinear iterations built around existing black-box CFD codes can be used to (1) improve convergence rates, (2) compute unstable steady-state solutions, (3) recover from divergence due to unsuitable initializations, and (4) diagnose convergence stagnation problems. The applications use both university and production codes applied to CFD problems arising in jet engine design.