Applications of numerical conformal mapping

Daniel I. Meiron; Steven A. Orszag; Moshe Israeli

doi:10.1016/0021-9991(81)90215-1

Applications of numerical conformal mapping

Daniel I. Meiron, Steven A. Orszag, Moshe Israeli

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

The application of conformal mapping methods to the solution of free-surface flow problems is considered. Methods of numerical conformal mapping based on Fourier series are extended to handle efficiently problems with time-dependent boundaries. They are shown to be practicable only for moderately distorted geometries. Extensions of the Menikoff-Zemach method to "breaking" geometries are presented. These latter methods are robust at quite large distortions, but degrade prematurely in time-dependent problems at amplitudes smaller than achieved by our recent vortex methods.

Original language	English
Pages (from-to)	345-360
Number of pages	16
Journal	Journal of Computational Physics
Volume	40
Issue number	2
DOIs	https://doi.org/10.1016/0021-9991(81)90215-1
State	Published - Apr 1981
Externally published	Yes

Bibliographical note

Funding Information:
* This work was supported the General Hydromechanics NC@O14-80-C-0127.

Funding

* This work was supported the General Hydromechanics NC@O14-80-C-0127.

Funders	Funder number
Air Force Office of Scientific Research	77-3405
Naval Sea Systems Command

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10.1016/0021-9991(81)90215-1

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title = "Applications of numerical conformal mapping",

abstract = "The application of conformal mapping methods to the solution of free-surface flow problems is considered. Methods of numerical conformal mapping based on Fourier series are extended to handle efficiently problems with time-dependent boundaries. They are shown to be practicable only for moderately distorted geometries. Extensions of the Menikoff-Zemach method to {"}breaking{"} geometries are presented. These latter methods are robust at quite large distortions, but degrade prematurely in time-dependent problems at amplitudes smaller than achieved by our recent vortex methods.",

author = "Meiron, \{Daniel I.\} and Orszag, \{Steven A.\} and Moshe Israeli",

note = "Funding Information: * This work was supported the General Hydromechanics NC@O14-80-C-0127.",

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AU - Orszag, Steven A.

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PY - 1981/4

Y1 - 1981/4

N2 - The application of conformal mapping methods to the solution of free-surface flow problems is considered. Methods of numerical conformal mapping based on Fourier series are extended to handle efficiently problems with time-dependent boundaries. They are shown to be practicable only for moderately distorted geometries. Extensions of the Menikoff-Zemach method to "breaking" geometries are presented. These latter methods are robust at quite large distortions, but degrade prematurely in time-dependent problems at amplitudes smaller than achieved by our recent vortex methods.

AB - The application of conformal mapping methods to the solution of free-surface flow problems is considered. Methods of numerical conformal mapping based on Fourier series are extended to handle efficiently problems with time-dependent boundaries. They are shown to be practicable only for moderately distorted geometries. Extensions of the Menikoff-Zemach method to "breaking" geometries are presented. These latter methods are robust at quite large distortions, but degrade prematurely in time-dependent problems at amplitudes smaller than achieved by our recent vortex methods.

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Applications of numerical conformal mapping

Abstract

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