An efficient quasi‐Newton method for two‐dimensional steady free surface flow. (17th January 2020)

• Record Type: Journal Article
• Authors: Demeester, Toon; van Brummelen, E. Harald; Degroote, Joris
• Is Part Of: International journal for numerical methods in fluids. Volume 92:Number 7(2020)
• Page Start: 785
• Page End: 801
• Publication Date: 2020-01-17
• Subjects: fitting method -- free surface flow -- perturbation analysis -- quasi‐Newton; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4806
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: Steady free surface flows are of interest in the fields of marine and hydraulic engineering. Fitting methods are generally used to represent the free surface position with a deforming grid. Existing fitting methods tend to use time‐stepping schemes, which is inefficient for steady flows. There also exists a steady iterative method, but that one needs to be implemented with a dedicated solver. Therefore a new method is proposed to efficiently simulate two‐dimensional (2D) steady free surface flows, suitable for use in conjunction with black‐box flow solvers. The free surface position is calculated with a quasi‐Newton method, where the approximate Jacobian is constructed in a novel way by combining data from past iterations with an analytical model based on a perturbation analysis of a potential flow. The method is tested on two 2D cases: the flow over a bottom topography and the flow over a hydrofoil. For all simulations the new method converges exponentially and in few iterations. Furthermore, convergence is independent of the free surface mesh size for all tests. Abstract : A new method is proposed to efficiently simulate 2D steady free surface flows, suitable for use in conjunction with black‐box flow solvers. The free surface position is calculated with a quasi‐Newton method where the approximate Jacobian is constructed in a novel way. For all test cases the method converges exponentially and in few iterations, independent of the free surface mesh size.