Mathematical theory and simulations of thermoporoelasticity

Autor: Andro Mikelić, Thomas Wick, Cornelis J. van Duijn
Přispěvatelé: Eindhoven University of Technology, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Universitaet Hannover, Institut fur Angewandte Mathematik, ANR-19-CE05-0032,UPGEO,Changement d'échelle et simulation des flux de chaleur pour amélioer l'efficacité des systèmes géothermiques profonds(2019), ANR-11-IDEX-0007,Avenir L.S.E.,PROJET AVENIR LYON SAINT-ETIENNE(2011)
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Discretization
Computational Mechanics
General Physics and Astronomy
02 engineering and technology
System of linear equations
01 natural sciences
Discrete system
0203 mechanical engineering
Applied mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
0101 mathematics
[SDU.STU.HY]Sciences of the Universe [physics]/Earth Sciences/Hydrology
Mathematics
Fundamental theorem
Mechanical Engineering
[SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment
Thermoporoelasticity equations
Backward Euler method
Finite element method
Computer Science Applications
free energy and stability
010101 applied mathematics
Mathematical theory
020303 mechanical engineering & transports
heat convection by Darcy's velocity
monolithic numerical scheme
Mechanics of Materials
[PHYS.MECA.THER]Physics [physics]/Mechanics [physics]/Thermics [physics.class-ph]
Temporal discretization
Zdroj: Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering, Elsevier, In press
ISSN: 0045-7825
Popis: International audience; In this paper we study the equations of semi-linear thermoporoelasticity. Starting point is the dimensionless formulation in van Duijn et al [7] (C.J. van Duijn, A. Mikelić, M. F. Wheeler, T. Wick, Internat. J Engng Sci., Vol. 138, 2019), which was obtained by a formal two-scale expansion. Nonlinearities in the equations arise through the fluid viscosity and the thermal conductivity, both may depend on temperature , and through the coupling in the heat convection by the Darcy discharge in the energy equation. The coupled system of equations involves as unknowns the skeleton displacement, Darcy discharge, fluid pressure and temperature. We treat the system in its incremental (i.e. time-discrete) form. We prove existence by applying a fundamental theorem of Brézis on pseudo-monotone operators. Moreover we show that the free energy of the system acts as a Lyapunov functional. This yields global stability in the time-stepping process. Our theoretical results are substantiated with two-dimensional numerical tests using a monolithic formulation. Temporal dis-cretization is based on the backward Euler scheme and finite elements are employed for the spatial discretization. The semi-linear discrete system is solved with Newton's method. In the proposed numerical examples, different source terms are employed and spatial mesh refinement studies show computational convergence.
Databáze: OpenAIRE
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