SOLUTION OF BOUNDARY PROBLEMS FOR THE LAPLACE EQUATION BY THE METHOD OF CONFORMING GRIDS,

Abstract

The solution of linear and nonlinear boundary-value problems for a two-dimensional Laplace equation with a curvilinear boundary is considered, using the theory of conformal mapping and the method of lines. The determination of the unknown arbitrary constants is reduced to the solution of a system of linear equations. The solution by the use of the obtained family of straight lines in the plane corresponds to the solution using the one-parameter family of curves. It is pointed out that such boundary value problems are encountered in physicochemical hydrodynamics. As an illustration of the method presented, the calculation of the current distribution in an electrolytic cell having the form of the annular sector and with isolated walls is presented.

Document Details

Document Type
Technical Report
Publication Date
Jan 30, 1969
Accession Number
AD0688726

Entities

People

  • V. T. Ivanov

Organizations

  • National Air and Space Intelligence Center

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Cartography
  • Cells
  • Conformal Mapping
  • Electrolytic Cells
  • Equations
  • Hydrodynamics
  • Mathematics
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)