Systems of nonlinear conservation laws. Final report, 1 Jun 88-31 May 91

Technical Report · Thu Jun 06 04:00:00 EDT 1991

OSTI ID:5237779

Shearer, M

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 2 {times} 2 systems of hyperbolic conservation laws with quadratic nonlinearities identifies four different types of equations. The Riemann problem was solved in detail 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 undercompressive shocks, which are physical shock waves closely associated with systems that change type.

• Research Organization: North Carolina State Univ., Raleigh, NC (United States)
• OSTI ID: 5237779
• Report Number(s): AD-A-238757/9/XAB; CNN: DAAL03-88-K-0080
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
DIFFERENTIAL EQUATIONS
DIFFERENTIAL GEOMETRY
EQUATIONS
FLOW MODELS
FLUID FLOW
GEOMETRY
GRANULAR MATERIALS
MASS
MASS TRANSFER
MATERIALS
MATHEMATICAL MODELS
MATHEMATICS
MECHANICS
MOMENTUM TRANSFER
MULTIPHASE FLOW
OIL WELLS
PARTIAL DIFFERENTIAL EQUATIONS
SHOCK WAVES
SOIL MECHANICS
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
WELLS