Regularized Chapman-Enskog expansion for scalar conservation laws. Final report

Technical Report · Mon Oct 01 04:00:00 EDT 1990

OSTI ID:6095280

Schochet, S; Tadmor, E

Rosenau has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. The behavior of Rosenau regularization of the Chapman-Enskog expansion (RCE) is studied in the context of scalar conservation laws. It is shown that thie RCE model retains the essential properties of the usual viscosity approximation, e.g., existence of traveling waves, monotonicity, upper-Lipschitz continuity..., and at the same time, it sharpens the standard viscous shock layers. It is proved that the regularized RCE approximation converges to the underlying inviscid entropy solution as its mean-free-path epsilon approaches 0, and the convergence rate is estimated.

• Research Organization: National Aeronautics and Space Administration, Hampton, VA (USA). Inst. for Computer Applications in Science and Engineering
• OSTI ID: 6095280
• Report Number(s): N-91-13966; NASA-CR--187441; ICASE--90-68; NAS--1.26:187441; CNN: NAS1-18605
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAPMAN-ENSKOG THEORY
COLLISIONS
CONSERVATION LAWS
CONVERGENCE
DATA
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
ENTROPY
EQUATIONS
FLUID FLOW
FLUID MECHANICS
HYDRODYNAMICS
IDEAL FLOW
INFORMATION
MATHEMATICAL MODELS
MEAN FREE PATH
MECHANICS
NAVIER-STOKES EQUATIONS
NUMERICAL DATA
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
PROGRESS REPORT
SCALARS
SHOCK WAVES
THEORETICAL DATA
THERMODYNAMIC PROPERTIES
VISCOSITY