The 2-dimensional Riemann problem for a 2 × 2 hyperbolic conservation law I. Isotropic media

Woonjae Hwang, W. Brent Lindquist

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We construct the solutions for a two-dimensional (2-D) Riemann problem for a 2 × 2 hyperbolic nonlinear system based upon the Keyfitz-Kranzer-Isaacson-Temple model. The system is applicable to polymer flooding of an oil reservoir; the parameterization can be adjusted to model either isotropic or anisotropic media. For isotropic media, the solutions are obtained by two methods. The first method utilizes a transformation into a one-dimensional (1-D) Cauchy problem. Such a transformation requires conformity of the x- and y-directional fluxes in the system. The second method involves a 2-D constructive technique which can be used more generally for solving systems. For the isotropic media case, we explicitly construct solutions for the so-called single and four quadrant Riemann problems by both methods and demonstrate the equality of the solutions. This has relevance as a test for the 2-D solution method, as existence and uniqueness results for solutions of systems in 1-D are known, whereas no such results exist for systems in 2-D.

Original languageEnglish
Pages (from-to)341-358
Number of pages18
JournalSIAM Journal on Mathematical Analysis
Volume34
Issue number2
DOIs
StatePublished - 2003

Keywords

  • Conservation law
  • Hyperbolic systems
  • Riemann problems

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