Self-Similar Fluid Dynamic Limits for the Broadwell System

Abstract

This report discusses a new approach for the resolution of the fluid dynamic limit for the Broadwell system of the kinetic theory of gases, appropriate in the case of Riemann, Maxwellian data. Since the formal limiting system is expected to have self-similar solutions, we are motivated to replace the Knudsen number E in the Broadwell model so that the resulting model admits self-similar solutions in E = x/t and then let E go to zero. The limiting, procedure is justified and the resulting limit is a solution of the Riemann problem for the fluid dynamic limit equations. A class of Riemann data for which this program can be carried out is exhibited. Furthermore it is shown that for the Carleman model the complete program can be done successfully for arbitrary Riemann data.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1992
Accession Number
ADA257950

Entities

People

  • Athanasios E. Tzavaras
  • Marshall Slemrod

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • C4I

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Continuity
  • Differential Equations
  • Equations
  • Kinetic Theory
  • Knudsen Number
  • Laser Peening
  • Mean Free Path
  • Navier Stokes Equations
  • Notation
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.
  • Mathematical Modeling and Probability Theory.