An efficient quasi-Newton method for two-dimensional steady free surface flow

Toon Demeester (Corresponding author), E. Harald van Brummelen, Joris Degroote

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)785-801
Number of pages17
JournalInternational Journal for Numerical Methods in Fluids
Issue number7
Early online date9 Jan 2020
Publication statusPublished - 1 Jul 2020


  • fitting method
  • free surface flow
  • perturbation analysis
  • quasi-Newton


Dive into the research topics of 'An efficient quasi-Newton method for two-dimensional steady free surface flow'. Together they form a unique fingerprint.

Cite this