Global Riemann solvers for several 3 × 3 systems of conservation laws with degeneracies

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study several 3 × 3 systems of conservation laws, arising in the modeling of two-phase flow with rough porous media and traffic flow with rough road condition. These systems share several features. The systems are of mixed type, with various degeneracies. Some families are linearly degenerate, while others are not genuinely nonlinear. Furthermore, along certain curves in the domain, the eigenvalues and eigenvectors of different families coincide. Most interestingly, in some suitable Lagrangian coordinate, the systems are partially decoupled, where some unknowns can be solved independently of the others. Finally, in special cases, the systems reduce to some 2 × 2 models, which have been studied in the literature. Utilizing the insights gained from these features, we construct global Riemann solvers for all these models. Possible treatments on the Cauchy problems are also discussed.

Original languageEnglish (US)
Pages (from-to)1599-1626
Number of pages28
JournalMathematical Models and Methods in Applied Sciences
Volume28
Issue number8
DOIs
StatePublished - Jul 1 2018

Fingerprint

Riemann Solvers
Systems of Conservation Laws
Conservation
Eigenvalues and eigenfunctions
Two phase flow
Rough
Porous materials
Porous Media Flow
Lagrangian Coordinates
Eigenvalues and Eigenvectors
Two-phase Flow
Traffic Flow
Cauchy Problem
Linearly
Unknown
Curve
Modeling
Model
Family

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

Cite this

@article{04a44015d06948a19b924268d4bbe37c,
title = "Global Riemann solvers for several 3 × 3 systems of conservation laws with degeneracies",
abstract = "We study several 3 × 3 systems of conservation laws, arising in the modeling of two-phase flow with rough porous media and traffic flow with rough road condition. These systems share several features. The systems are of mixed type, with various degeneracies. Some families are linearly degenerate, while others are not genuinely nonlinear. Furthermore, along certain curves in the domain, the eigenvalues and eigenvectors of different families coincide. Most interestingly, in some suitable Lagrangian coordinate, the systems are partially decoupled, where some unknowns can be solved independently of the others. Finally, in special cases, the systems reduce to some 2 × 2 models, which have been studied in the literature. Utilizing the insights gained from these features, we construct global Riemann solvers for all these models. Possible treatments on the Cauchy problems are also discussed.",
author = "Wen Shen",
year = "2018",
month = "7",
day = "1",
doi = "10.1142/S0218202518500446",
language = "English (US)",
volume = "28",
pages = "1599--1626",
journal = "Mathematical Models and Methods in Applied Sciences",
issn = "0218-2025",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "8",

}

Global Riemann solvers for several 3 × 3 systems of conservation laws with degeneracies. / Shen, Wen.

In: Mathematical Models and Methods in Applied Sciences, Vol. 28, No. 8, 01.07.2018, p. 1599-1626.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Global Riemann solvers for several 3 × 3 systems of conservation laws with degeneracies

AU - Shen, Wen

PY - 2018/7/1

Y1 - 2018/7/1

N2 - We study several 3 × 3 systems of conservation laws, arising in the modeling of two-phase flow with rough porous media and traffic flow with rough road condition. These systems share several features. The systems are of mixed type, with various degeneracies. Some families are linearly degenerate, while others are not genuinely nonlinear. Furthermore, along certain curves in the domain, the eigenvalues and eigenvectors of different families coincide. Most interestingly, in some suitable Lagrangian coordinate, the systems are partially decoupled, where some unknowns can be solved independently of the others. Finally, in special cases, the systems reduce to some 2 × 2 models, which have been studied in the literature. Utilizing the insights gained from these features, we construct global Riemann solvers for all these models. Possible treatments on the Cauchy problems are also discussed.

AB - We study several 3 × 3 systems of conservation laws, arising in the modeling of two-phase flow with rough porous media and traffic flow with rough road condition. These systems share several features. The systems are of mixed type, with various degeneracies. Some families are linearly degenerate, while others are not genuinely nonlinear. Furthermore, along certain curves in the domain, the eigenvalues and eigenvectors of different families coincide. Most interestingly, in some suitable Lagrangian coordinate, the systems are partially decoupled, where some unknowns can be solved independently of the others. Finally, in special cases, the systems reduce to some 2 × 2 models, which have been studied in the literature. Utilizing the insights gained from these features, we construct global Riemann solvers for all these models. Possible treatments on the Cauchy problems are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=85050163215&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050163215&partnerID=8YFLogxK

U2 - 10.1142/S0218202518500446

DO - 10.1142/S0218202518500446

M3 - Article

AN - SCOPUS:85050163215

VL - 28

SP - 1599

EP - 1626

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 8

ER -