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ABSTRACT This work proposes a novel approach for coupling non‐isothermal fluid dynamics with fracture mechanics to capture thermal effects within fluid‐filled fractures accurately. This method addresses critical aspects of calculating fracture width in enhanced geothermal systems, where the temperature effects of fractures are crucial. The proposed algorithm features an iterative coupling between an interface‐capturing phase‐field fracture method and interface‐tracking thermo‐fluid‐structure interaction using arbitrary Lagrangian–Eulerian coordinates. We use a phase‐field approach to represent fractures and reconstruct the geometry to frame a thermo‐fluid‐structure interaction problem, resulting in pressure and temperature fields that drive fracture propagation. We developed a novel phase‐field interface model accounting for thermal effects, enabling the coupling of quantities specific to the fluid‐filled fracture with the phase‐field model through the interface between the fracture and the intact solid domain. We provide several numerical examples to demonstrate the capabilities of the proposed algorithm. In particular, we analyze mesh convergence of our phase‐field interface model, investigate the effects of temperature on crack width and volume in a static regime, and highlight the method's potential for modeling slowly propagating fractures. 

In this work, we review and describe our computational framework for solving multiphysics phase-field fracture problems in porous media. Therein, the following five coupled nonlinear physical models are addressed: displacements (geo-mechanics), a phase-field variable to indicate the fracture position, a pressure equation (to describe flow), a proppant concentration equation, and/or a saturation equation for two-phase fracture flow, and finally a finite element crack width problem. The overall coupled problem is solved with a staggered solution approach, known in subsurface modeling as the fixed-stress iteration. A main focus is on physics-based discretizations. Galerkin finite elements are employed for the displacement-phase-field system and the crack width problem. Enriched Galerkin formulations are used for the pressure equation. Further enrichments using entropy-vanishing viscosity are employed for the proppant and/or saturation equations. A robust and efficient quasi-monolithic semi-smooth Newton solver, local mesh adaptivity, and parallel implementations allow for competitive timings in terms of the computational cost. Our framework can treat two- and three-dimensional realistic field and laboratory examples. The resulting program is an in-house code named IPACS (Integrated Phase-field Advanced Crack Propagation Simulator) and is based on the finite element library deal.II. Representative numerical examples are included in this document.