# Accession Number:

## ADA229138

# Title:

## Regularized Chapman-Enskog Expansion for Scalar Conservation Laws

# Descriptive Note:

## Final rept.,

# Corporate Author:

## INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

# Personal Author(s):

# Report Date:

## 1990-10-01

# Pagination or Media Count:

## 18.0

# Abstract:

Rosenau Phys. Rev. A, 40 1989, pp. 7193-6 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. This paper studies the behavior of Rosenau regularization of the Chapman-Enskog expansion R-C-E in the context of scalar conservation laws. It is shown that this R-C-E model retains the essential properties of the usual viscosity approximation, e. g., existence of travelling waves, monotonicity, upper-Lipschitz continuity etc. , and at the same time, it sharpens the standard viscous shock layers. We prove that the regularized R-C-E approximation converges to the underlying inviscid entropy solution as its mean-free-path epsilon decreases monotonically to a limit and we estimate the convergence rate. KR

# Descriptors:

# Subject Categories:

- Fluid Mechanics