Even-Parity S_(N) Adjoint Method Including SP_(N) Model Error and Iterative Efficiency

Abstract

In this Dissertation, we analyze an adjoint-based approach for assessing the model error of SP_(N) equations (low fidelity model) by comparing it against S_(N) equations (high fidelity model). Three model error estimation methods, namely, direct , residual, and adjoint methods are proposed. In order to compare the SP_(N) solution against S_(N), we also proposed angular intensity reconstruction schemes for reconstructing S_(N) angular intensity from SP_(N) solutions. The methodology is then applied to a vehicle atmosphere re-entry problem and the convergence behavior of the SP_(N) and Even-parity S_(N) are compared with that of the Least-squares S_(N) method. The results show that all the three model error estimation methods are equivalent up to a readily computable compensation and the Least-squares S_(N) method is far superior than the Even-parity S_(N) and SP_(N) methods when applied to such a near-void problem. Various forms of SP_(N) equations, together with their appropriate iterative solution schemes and acceleration techniques are evaluated in terms of iterative efficiency. The Fourier analyses and numerical test results indicate the Canonical form solved with DSA or AnMG preconditioned source iteration offering the best iterative performance.