Systems of Nonlinear Conservation Laws
Final rept. 1 Jun 88-31 May 91,
NORTH CAROLINA STATE UNIV AT RALEIGH
Pagination or Media Count:
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.
- Numerical Mathematics