A Boundary Integral Method for Two-Dimensional Water Waves

Abstract

A boundary integral solution to the two-dimensional, free-surface water wave problem is presented. The mathematical formulation involves application of potential theory and appropriate initial and boundary conditions to resolve the progression of the linear free-surface waves. The solution to the potential flow problem is represented, through Green's theorem, by a boundary integral method that is approximated via linear boundary panels. The resulting system of algebraic equations is solved for required flow parameters. The free surface is tracked at each time level by numerical integration of the linearized free-surface boundary conditions. Despite the use of linear panels, numerical results compare favorably with the exact linear theory and indicate that the computational scheme is able to track the development and propagation of steep waves over long periods of time. An analysis is also provided to aid in the development and numerical implementation of artificial or perfectly absorbing boundary conditions at the vertical, imaginary, truncated boundaries.

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Document Details

Document Type
Technical Report
Publication Date
Oct 31, 1997
Accession Number
ADA637056

Entities

People

  • Isaac M. Kuria
  • Steven A. Trogdon

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Flow
  • Geometry
  • Integrals
  • Numerical Analysis
  • Numerical Integration
  • Potential Flow
  • Surface Waters
  • Surface Waves
  • Theorems
  • Two Dimensional
  • Water Waves
  • Waves

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Linear Algebra