We consider a general Euler-type two-phase flow model with relaxation towards phase equilibrium. We provide a complete description of the transition between the wave dynamics of the homogeneous relaxation system and that of the local equilibrium approximation. In particular, we present generally valid analytical expressions for the amplifications and velocities of each Fourier component. This transitional wave dynamics is fully determined by only two dimensionless parameters; a stiffness parameter and the ratio of the sound velocities in the stiff and non-stiff limits. A direct calculation verifies that the stability criterion is precisely the subcharacteristic condition. We further prove a maximum principle in the transitional regime, similar in spirit to the subcharacteristic condition; the transitional wave speeds can never exceed the largest wave speed of the homogeneous relaxation system. Finally, we identify the existence of a critical region of wave numbers where the sonic waves completely disappear from the system. This region corresponds to the casus irreducibilis of the describing cubic polynomial.
DOI : 10.1051/m2an/2014048
Mots-clés : Relaxation, subcharacteristic condition, phase transfer
@article{M2AN_2015__49_2_601_0,
author = {Solem, Susanne and Aursand, Peder and Fl\r{a}tten, Tore},
title = {The dispersive wave dynamics of a two-phase flow relaxation model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {601--619},
publisher = {EDP-Sciences},
volume = {49},
number = {2},
year = {2015},
doi = {10.1051/m2an/2014048},
mrnumber = {3342220},
zbl = {1316.35193},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014048/}
}
TY - JOUR AU - Solem, Susanne AU - Aursand, Peder AU - Flåtten, Tore TI - The dispersive wave dynamics of a two-phase flow relaxation model JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 601 EP - 619 VL - 49 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014048/ DO - 10.1051/m2an/2014048 LA - en ID - M2AN_2015__49_2_601_0 ER -
%0 Journal Article %A Solem, Susanne %A Aursand, Peder %A Flåtten, Tore %T The dispersive wave dynamics of a two-phase flow relaxation model %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 601-619 %V 49 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014048/ %R 10.1051/m2an/2014048 %G en %F M2AN_2015__49_2_601_0
Solem, Susanne; Aursand, Peder; Flåtten, Tore. The dispersive wave dynamics of a two-phase flow relaxation model. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 2, pp. 601-619. doi : 10.1051/m2an/2014048. http://www.numdam.org/articles/10.1051/m2an/2014048/
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