An organizing center for wave bifurcation in multiphase flow models

Journal Article · Wed Oct 01 04:00:00 EDT 1997 · SIAM Journal of Applied Mathematics

DOI:https://doi.org/10.1137/S0036139995280683· OSTI ID:561976

Marchesin, D ^[1]; Plohr, B J ^[2]; Schecter, S ^[3]

---

1. Inst. de Matematica Pura e Aplicada, Rio de Janeiro (Brazil)
2. State Univ. of New York, Stony Brook, NY (United States)
3. North Carolina State Univ., Raleigh, NC (United States). Mathematics Dept.

The authors consider a one-parameter family of nonstrictly hyperbolic systems of conservation laws modeling three-phase flow in a porous medium. For a particular value of the parameter, the model has a shock wave solution that undergoes several bifurcations upon perturbation of its left and right states and the parameter. In this paper they use singularity theory and bifurcation theory of dynamical systems, including Melnikov`s method, to find all nearby shock waves that are admissible according to the viscous profile criterion. They use these results to construct a unique solution of the Riemann problem for each left and right state and parameter value in a neighborhood of the unperturbed shock wave solution; together with previous numerical work, this construction completes the solution of the three-phase flow model. In the bifurcation analysis, the unperturbed shock wave acts as an organizing center for the waves appearing in Riemann solutions.

• Sponsoring Organization: Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Sao Paulo, SP (Brazil); National Science Foundation, Washington, DC (United States); Department of the Army, Washington, DC (United States); USDOE, Washington, DC (United States)
• DOE Contract Number: FG02-90ER25084
• OSTI ID: 561976
• Journal Information: SIAM Journal of Applied Mathematics, Journal Name: SIAM Journal of Applied Mathematics Journal Issue: 5 Vol. 57; ISSN SMJMAP; ISSN 0036-1399
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
BIFURCATION
FLOW MODELS
MULTIPHASE FLOW
POROUS MATERIALS
SHOCK WAVES