A monolithic homotopy continuation algorithm with application to computational fluid dynamics

作者：Brown David A^*; Zingg David W

来源：Journal of Computational Physics, 2016, 321: 55-75.

DOI：10.1016/j.jcp.2016.05.031

• Homotopy
• Continuation
• Globalization
• Newton-Krylov
• Computational fluid dynamics

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.

• 出版日期2016-9-15