Regularized Chapman-Enskog Expansion for Scalar Conservation Laws
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1990
- Accession Number
- ADA229138
Entities
People
- Eitan Tadmor
- Steven Schochet