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.
Keywords: nonhyperbolic balance laws, incompressible two-fluid flow
@article{M2AN_2005__39_1_37_0,
author = {Sever, Michael},
title = {Solutions of a nonhyperbolic pair of balance laws},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {37--58},
year = {2005},
publisher = {EDP Sciences},
volume = {39},
number = {1},
doi = {10.1051/m2an:2005003},
mrnumber = {2136199},
zbl = {1080.35092},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2005003/}
}
TY - JOUR AU - Sever, Michael TI - Solutions of a nonhyperbolic pair of balance laws JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 37 EP - 58 VL - 39 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2005003/ DO - 10.1051/m2an:2005003 LA - en ID - M2AN_2005__39_1_37_0 ER -
%0 Journal Article %A Sever, Michael %T Solutions of a nonhyperbolic pair of balance laws %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 37-58 %V 39 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2005003/ %R 10.1051/m2an:2005003 %G en %F M2AN_2005__39_1_37_0
Sever, Michael. Solutions of a nonhyperbolic pair of balance laws. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 1, pp. 37-58. doi: 10.1051/m2an:2005003
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