Wave Structure Induced by Fluid Dynamic Limits in the Broadwell Model

Abstract

Consider the fluid dynamic limit problem for the Broadwell system of the kinetic theory of gases, for Riemann, Maxwellian initial data. The formal limit is the Riemann problem for a pair of conservation laws and is invariant under dilations of coordinates. The approach of self-similar fluid dynamic limits consists in replacing the mean free path in the Broadwell model so that the resulting problem preserves the invariance under dilations. The limiting procedure was justified in ST. Here, we study the structure of the emerging solutions. We show that they consist of two wave fans separated by a constant state. Each wave fan is associated with one of the characteristic fields and is either a rarefaction wave or a shock wave. The shocks satisfy the Lax shock conditions and have the internal structure of a Broadwell shock profile.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1993
Accession Number
ADA268512

Entities

People

  • Athanasios E. Tzavaras

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Boundary Value Problems
  • Cauchy Problem
  • Collisions
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Euler Equations
  • Geometry
  • Kinetic Theory
  • Mean Free Path
  • Nonlinear Systems
  • Notation
  • Real Variables
  • Shock Waves
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.