# Solutions of a nonhyperbolic pair of balance laws

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 39, Issue: 1, page 37-58
- ISSN: 0764-583X

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topSever, Michael. "Solutions of a nonhyperbolic pair of balance laws." ESAIM: Mathematical Modelling and Numerical Analysis 39.1 (2010): 37-58. <http://eudml.org/doc/194257>.

@article{Sever2010,

abstract = {
We describe a constructive algorithm for obtaining smooth
solutions of a nonlinear, nonhyperbolic pair of balance laws
modeling incompressible two-phase flow in one space dimension and
time. Solutions are found as stationary solutions of a related
hyperbolic system, based on the introduction of an artificial time
variable.
As may be expected for such nonhyperbolic systems, in general the
solutions obtained do not satisfy both components of the given
initial data. This deficiency may be overcome, however, by
introducing an alternative “solution" satisfying both components
of the initial data and an approximate form of a corresponding
linearized system.
},

author = {Sever, Michael},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Nonhyperbolic balance laws; incompressible two-fluid flow.; algorithm; smooth solutions; incompressible two-phase flow; hyperbolic system},

language = {eng},

month = {3},

number = {1},

pages = {37-58},

publisher = {EDP Sciences},

title = {Solutions of a nonhyperbolic pair of balance laws},

url = {http://eudml.org/doc/194257},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Sever, Michael

TI - Solutions of a nonhyperbolic pair of balance laws

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 1

SP - 37

EP - 58

AB -
We describe a constructive algorithm for obtaining smooth
solutions of a nonlinear, nonhyperbolic pair of balance laws
modeling incompressible two-phase flow in one space dimension and
time. Solutions are found as stationary solutions of a related
hyperbolic system, based on the introduction of an artificial time
variable.
As may be expected for such nonhyperbolic systems, in general the
solutions obtained do not satisfy both components of the given
initial data. This deficiency may be overcome, however, by
introducing an alternative “solution" satisfying both components
of the initial data and an approximate form of a corresponding
linearized system.

LA - eng

KW - Nonhyperbolic balance laws; incompressible two-fluid flow.; algorithm; smooth solutions; incompressible two-phase flow; hyperbolic system

UR - http://eudml.org/doc/194257

ER -

## References

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- H. Ransom and D.L. Hicks, Hyperbolic two-pressure models for two-phase flow . J. Comput. Phys.53 (1984) 124–151. Zbl0537.76070
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