Mats Kirkesæther Brun

• Brun, Mats Kirkesæther; Ahmed, Elyes; Berre, Inga; Nordbotten, Jan Martin & Radu, Florin Adrian (2020). Monolithic and splitting solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport. Computers and Mathematics with Applications.  ISSN 0898-1221.  80(8), s 1964- 1984 . doi: 10.1016/j.camwa.2020.08.022 Fulltekst i vitenarkiv. Vis sammendrag

  This paper concerns monolithic and splitting-based iterative procedures for the coupled nonlinear thermo-poroelasticity model problem. The thermo-poroelastic model problem we consider is formulated as a three-field system of PDE’s, consisting of an energy balance equation, a mass balance equation and a momentum balance equation, where the primary variables are temperature, fluid pressure, and elastic displacement. Due to the presence of a nonlinear convective transport term in the energy balance equation, it is convenient to have access to both the pressure and temperature gradients. Hence, we introduce these as two additional variables and extend the original three-field model to a five-field model. For the numerical solution of this five-field formulation, we compare six approaches that differ by how we treat the coupling/decoupling between the flow and/from heat and/from the mechanics, suitable for varying coupling strength between the three physical processes. The approaches have in common a simultaneous application of the so-called -scheme, which works both to stabilize iterative splitting as well as to linearize nonlinear problems, and can be seen as a generalization of the Undrained and Fixed-Stress Split algorithms. More precisely, the derived procedures transform a nonlinear and fully coupled problem into a set of simpler subproblems to be solved sequentially in an iterative fashion. We provide a convergence proof for the derived algorithms, and demonstrate their performance through several numerical examples investigating different strengths of the coupling between the different processes.

• Brun, Mats Kirkesæther; Wick, Thomas; Berre, Inga; Nordbotten, Jan Martin & Radu, Florin Adrian (2020). An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters. Computer Methods in Applied Mechanics and Engineering.  ISSN 0045-7825.  361:112752, s 1- 22 . doi: 10.1016/j.cma.2019.112752
• Brun, Mats Kirkesæther; Ahmed, Elyes; Nordbotten, Jan Martin & Radu, Florin Adrian (2019). Well-posedness of the fully coupled quasi-static thermo-poroelastic equations with nonlinear convective transport. Journal of Mathematical Analysis and Applications.  ISSN 0022-247X.  471(1-2), s 239- 266 . doi: 10.1016/j.jmaa.2018.10.074 Fulltekst i vitenarkiv.
• Brun, Mats Kirkesæther; Berre, Inga; Nordbotten, Jan Martin & Radu, Florin Adrian (2018). Upscaling of the coupling of hydromechanical and thermal processes in a quasi-static poroelastic medium. Transport in Porous Media.  ISSN 0169-3913.  124(1), s 137- 158 . doi: 10.1007/s11242-018-1056-8 Fulltekst i vitenarkiv.
• Brun, Mats Kirkesæther & Kalisch, Henrik (2018). Convective wave breaking in the KdV equation. Analysis and Mathematical Physics.  ISSN 1664-2368.  8(1), s 57- 75 . doi: 10.1007/s13324-017-0163-y

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• Brun, Mats Kirkesæther; Ahmed, Elyes; Radu, Florin Adrian; Berre, Inga & Nordbotten, Jan Martin (2019). Monolithic and Splitting Based Solution Schemes for Nonlinear Quasi-static Thermo-poroelasticity.
• Brun, Mats Kirkesæther; Radu, Florin Adrian; Berre, Inga & Nordbotten, Jan Martin (2019). Upscaling, analysis, and iterative numerical solution schemes for thermo-poroelasticity.
• Brun, Mats Kirkesæther; Radu, Florin Adrian; Berre, Inga; Nordbotten, Jan Martin & Ahmed, Elyes (2018). Upscaling of coupled geomechanics, flow, and heat in a poroelastic medium in the quasi-static situation..

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