Systems of Nonlinear Conservation Laws

Abstract

Research in Plastic flow in two and three dimensions focused on the issue of loss of stability and well posedness in the equations of motion of granular materials. The partial differential equations are derived from conservation of mass and momentum, augmented by constitutive laws that relate the dependent variables algebraically. The starting point was the motion in two dimensions of a rigid-plastic material, with the constitutive laws coming from critical state soil mechanics. Hyperbolic conservation laws gave the classification of 2x2 systems of hyperbolic conservation laws with quadratic nonlinearities identifies four different types of equations. The Riemann problem was solved in detail in for three of the four types. The fourth type of equation, Case I, is the most significant for applications to models of multiphase flow in oil reservoirs. This case involves under compressive shocks, which are physical shock waves closely associated with systems that change type.

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Document Details

Document Type
Technical Report
Publication Date
Jun 06, 1991
Accession Number
ADA238757

Entities

People

  • Michael Shearer

Organizations

  • North Carolina State University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Cauchy Problem
  • Classification
  • Computational Science
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Flow
  • Granular Materials
  • Materials
  • Mechanical Properties
  • Mechanics
  • Military Research
  • North Carolina
  • Partial Differential Equations
  • Plastic Flow
  • Soil Mechanics

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.
  • Theoretical Analysis.