An Algorithm for a Hyperbolic Free Boundary Problem.

Abstract

In this report, which is the first part of a more comprehensive work, a solution algorithm is given for a hyperbolic conservation law. The algorithm is of an embedding type in that the solution is built up from Green's functions for simple processes taking place without reference to boundaries, and the locations of shocks are not explicitly followed. There is a discussion of boundary conditions and treatment of the Burgers and Korteweg-de Vries equations. Cursory mention is made of the extension to systems. Appropriate function spaces for solutions are introduced. The effects of perturbations in the initial conditions and of the velocity of propagation of disturbances are analyzed. For a monotonic velocity profile, in the one-dimensional case without boundaries, a convergence proof and error estimate are given.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA045512

Entities

People

  • J. C. W. Rogers

Organizations

  • Johns Hopkins University

Tags

Communities of Interest

  • Air Platforms
  • Counter IED
  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boltzmann Equation
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Continuity
  • Convection
  • Differential Equations
  • Distribution Functions
  • Equations
  • Fluid Dynamics
  • Fluid Flow
  • Military Research
  • Naval Architecture
  • Numbers
  • Physics Laboratories
  • Turbulence

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Calculus or Mathematical Analysis
  • Systems Analysis and Design

Technology Areas

  • Space