Mathematical theory and simulations of thermoporoelasticity - Archive ouverte HAL Access content directly
Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2020

Mathematical theory and simulations of thermoporoelasticity

(1) , (2) , (3)


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.
Fichier principal
Vignette du fichier
SemiLinearThermoporoelasticityv10.pdf (2.55 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02429820 , version 1 (06-01-2020)



Cornelis J van Duijn, Andro Mikelic, Thomas Wick. Mathematical theory and simulations of thermoporoelasticity. Computer Methods in Applied Mechanics and Engineering, inPress, ⟨10.1016/j.cma.2020.113048⟩. ⟨hal-02429820⟩
395 View
201 Download



Gmail Facebook Twitter LinkedIn More