An Alternative Complex Boundary Element Method for Nonlinear Free Surface Problems

Abstract

A complex variable boundary element method is developed for potential flow problems by applying Cauchy's integral theorem to the complex velocity. The resulting integral equation is a function of the normal and tangential velocity components on the boundary. A new form of the full nonlinear dynamic free surface boundary condition is used to describe the evolution of tangential velocities. This alternate method solves for flows with field singularities more easily than the conventional method, which uses the complex velocity potential. Also, the velocity field is given directly without the need for numerical differentiation. Under the new formulation, the dynamic free surface boundary condition does, however, become more complicated. As a result, while the new form of the boundary element method has definite advantages for fixed boundaries, its usefulness for free surface problems is mixed.

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Document Details

Document Type
Technical Report
Publication Date
Feb 24, 1988
Accession Number
ADA250817

Entities

People

  • S. W. Hong
  • W. P. Graebel
  • W. W. Schultz

Organizations

  • University of Michigan

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Applied Mechanics
  • Boundary Element Methods
  • Boundary Value Problems
  • Complex Variables
  • Computations
  • Conformal Mapping
  • Coordinate Systems
  • Energy Conservation
  • Engineering
  • Equations
  • Integral Equations
  • Marine Engineering
  • Materials
  • Naval Architecture
  • Stratified Fluids
  • Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.