Details
| Original language | English |
|---|---|
| Pages (from-to) | 4267-4293 |
| Number of pages | 27 |
| Journal | Applicable analysis |
| Volume | 101 |
| Issue number | 12 |
| Publication status | Published - 27 Jun 2022 |
Abstract
In this paper, we consider Mandel's problem in the context of nonlinear single-phase poroelasticity, where it is assumed that the fluid is sightly compressible and porosity and permeability are given functions of the volume strain. In the first part of the paper we prove well-posedness of the time-discrete incremental problem by recasting the equations in an abstract form involving a pseudo-monotone operator. Further, we show existence of a Lyapunov functional yielding a global time discrete solution. In the second part, we investigate numerically the behavior of the poroelastic structure. In particular, we verify the assumptions leading to Mandel's solution. We also demonstrate some consequences of the proposed nonlinearities.
Keywords
- benchmark, incompressible fluids and solids, Lyapunov functional, Mandel's problem, Nonlinear poroelasticity
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Applicable analysis, Vol. 101, No. 12, 27.06.2022, p. 4267-4293 .
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Mandel's problem as a benchmark for two-dimensional nonlinear poroelasticity
AU - van Duijn, C. J.
AU - Mikelić, A.
AU - Wick, T.
N1 - Funding Information: A. M. was partially supported by Darcy Center of Eindhoven University of Technology and Utrecht University, the Netherlands, by the project UPGEO 〈ANR-19-CU05-032 〉 of the French National Research Agency (ANR) and by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program ‘Investissements d'Avenir’ (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). The author deceased in Lyon on 28/11/2020.
PY - 2022/6/27
Y1 - 2022/6/27
N2 - In this paper, we consider Mandel's problem in the context of nonlinear single-phase poroelasticity, where it is assumed that the fluid is sightly compressible and porosity and permeability are given functions of the volume strain. In the first part of the paper we prove well-posedness of the time-discrete incremental problem by recasting the equations in an abstract form involving a pseudo-monotone operator. Further, we show existence of a Lyapunov functional yielding a global time discrete solution. In the second part, we investigate numerically the behavior of the poroelastic structure. In particular, we verify the assumptions leading to Mandel's solution. We also demonstrate some consequences of the proposed nonlinearities.
AB - In this paper, we consider Mandel's problem in the context of nonlinear single-phase poroelasticity, where it is assumed that the fluid is sightly compressible and porosity and permeability are given functions of the volume strain. In the first part of the paper we prove well-posedness of the time-discrete incremental problem by recasting the equations in an abstract form involving a pseudo-monotone operator. Further, we show existence of a Lyapunov functional yielding a global time discrete solution. In the second part, we investigate numerically the behavior of the poroelastic structure. In particular, we verify the assumptions leading to Mandel's solution. We also demonstrate some consequences of the proposed nonlinearities.
KW - benchmark
KW - incompressible fluids and solids
KW - Lyapunov functional
KW - Mandel's problem
KW - Nonlinear poroelasticity
UR - http://www.scopus.com/inward/record.url?scp=85133194451&partnerID=8YFLogxK
U2 - 10.1080/00036811.2022.2091992
DO - 10.1080/00036811.2022.2091992
M3 - Article
AN - SCOPUS:85133194451
VL - 101
SP - 4267
EP - 4293
JO - Applicable analysis
JF - Applicable analysis
SN - 0003-6811
IS - 12
ER -