TY - GEN
T1 - Asymptotic behavior of a solution of relaxation system for flow in porous media
AU - Abreu, E.
AU - Bustos, A.
AU - Lambert, W. J.
N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
PY - 2018
Y1 - 2018
N2 - We introduce a novel modeling of phase transitions in thermal flow in porous media by using hyperbolic system of balance laws, instead of system of conservation laws. We are interested in two different behaviors of the balance system: the long time behavior, in which we study the solution with fixed relaxation term and very large time; and the behavior of the solution when the relaxation term is taken to zero and the time is fixed. We also are interested in solving the question: “Does this balance system tend to the conservation system under equilibrium hypothesis?”. To answer this question, we introduce a projection technique for the wave groups appearing in the system of equations and we study the behavior of each group. For a particular Riemann datum, using the projection method, we show the existence of a decaying traveling profile supported by source terms and we analyze the behavior of this solution. We corroborate our analysis with numerical experiments.
AB - We introduce a novel modeling of phase transitions in thermal flow in porous media by using hyperbolic system of balance laws, instead of system of conservation laws. We are interested in two different behaviors of the balance system: the long time behavior, in which we study the solution with fixed relaxation term and very large time; and the behavior of the solution when the relaxation term is taken to zero and the time is fixed. We also are interested in solving the question: “Does this balance system tend to the conservation system under equilibrium hypothesis?”. To answer this question, we introduce a projection technique for the wave groups appearing in the system of equations and we study the behavior of each group. For a particular Riemann datum, using the projection method, we show the existence of a decaying traveling profile supported by source terms and we analyze the behavior of this solution. We corroborate our analysis with numerical experiments.
KW - Asymptotic expansion
KW - Balance laws
KW - Finite volume
KW - Flow in porous media
KW - Non-equilibrium relaxation
KW - Riemann problem
UR - http://www.scopus.com/inward/record.url?scp=85049378109&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-91545-6_2
DO - 10.1007/978-3-319-91545-6_2
M3 - Conference contribution
AN - SCOPUS:85049378109
SN - 9783319915449
T3 - Springer Proceedings in Mathematics and Statistics
SP - 15
EP - 28
BT - Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016
A2 - Westdickenberg, Michael
A2 - Klingenberg, Christian
PB - Springer New York LLC
T2 - 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
Y2 - 1 August 2016 through 5 August 2016
ER -