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

Abstract

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
JournalInternational Journal for Numerical Methods in Fluids
DOIs
Publication statusE-pub ahead of print - 9 Jan 2020

Fingerprint

Quasi-Newton Method
Free Surface Flow
Newton-Raphson method
Steady Flow
Free Surface
Iteration
Hydrofoils
Potential Flow
Potential flow
Perturbation Analysis
Time Stepping
Steady flow
Topography
Iterative methods
Black Box
Hydraulics
Analytical Model
Analytical models
Mesh
Tend

Keywords

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

Cite this

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title = "An efficient quasi-Newton method for two-dimensional steady free surface flow",
abstract = "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.",
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An efficient quasi-Newton method for two-dimensional steady free surface flow. / Demeester, Toon (Corresponding author); van Brummelen, E. Harald; Degroote, Joris.

In: International Journal for Numerical Methods in Fluids, 09.01.2020.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - van Brummelen, E. Harald

AU - Degroote, Joris

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