A monolithic homotopy continuation algorithm with application to computational fluid dynamics

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• 作者：David A. Brown ; ^{utiasdavid.brown@mail.utoronto.ca" class="auth_mail" title="E-mail the corresponding author} ; David W. Zingg
• 关键词：Homotopy ; Continuation ; Globalization ; Newton&ndash ; Krylov ; Computational fluid dynamics
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：321
• 期：Complete
• 页码：55-75
• 全文大小：852 K

文摘

A new class of homotopy continuation methods is developed suitable for globalizing quasi-Newton methods for large sparse nonlinear systems of equations. The new continuation methods, described as monolithic homotopy continuation, differ from the classical predictor–corrector algorithm in that the predictor and corrector phases are replaced with a single phase which includes both a predictor and corrector component. Conditional convergence and stability are proved analytically. Using a Laplacian-like operator to construct the homotopy, the new algorithm is shown to be more efficient than the predictor–corrector homotopy continuation algorithm as well as an implementation of the widely-used pseudo-transient continuation algorithm for some inviscid and turbulent, subsonic and transonic external aerodynamic flows over the ONERA M6 wing and the NACA 0012 airfoil using a parallel implicit Newton–Krylov finite-difference flow solver.