Transitional Waves for Conservation Laws
Abstract
A new class of fundamental waves arises in conservation laws that are not strictly hyperbolic. These waves serve as transitions between wave groups associated with particular characteristic families. Transitional shock waves are discontinuous solutions that possess viscous profiles but do not conform to the Lax characteristic criterion; they are sensitive to the precise form of the physical viscosity. Transitional rarefaction waves are rarefaction fans across which the characteristic family changes from faster to slower. This paper identifies an extensive family of transitional shock waves for conservation laws with quadratic fluxes and arbitrary viscosity matrices; this family comprises all transitional shock waves for certain class of such quadratic models. We also establish, for general systems for two conservation laws, the generic nature of rarefaction curves near an elliptic region, thereby identifying transitional rarefaction waves. The use of transitional waves in solving Riemann problems is illustrated in an example where the characteristic and viscous profile admissibility criteria yield distinct solutions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1988
- Accession Number
- ADA204094
Entities
People
- Bradley J. Plohr
- Dan Marchesin
- Eli L. Isaacson
Organizations
- University of Wisconsin–Madison