GReS: A Novel Prototyping Platform for Multi-Physics Problems with Multiple Domains and Fractures

  • Moretto, Daniele (Università di Padova)
  • Da Silva Castro, Eduardo (Università di Padova)
  • Franceschini, Andrea (Università di Padova)
  • Ferronato, Massimiliano (Università di Padova)

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The growing availability of computational resources has significantly increased the scientific community’s interest in performing complex multi-physics and multi-domain simulations. In this context, we present GReS, a novel open-source platform specifically designed as a prototyping environment for the development and testing of numerical algorithms aimed at solving fully coupled multi-physics and multi-domain problems. GReS enables the decomposition of the global computational domain into possibly non-conforming subdomains, where different physical models can be employed, including solid mechanics, saturated and unsaturated fluid flow, and heat transfer. To enforce coupling of the solution at the subdomain interfaces, the code relies on lower-dimensional interface solvers based on the mortar method and equipped with some interface law, such as simple mesh tying or non-linear contact mechanics. This framework provides great flexibility in the treatment of multi-physics problems with non-standard geometrical configurations. The platform is developed in a high-level programming environment (MATLAB), which lowers the entry barrier for both new users and developers and significantly reduces the effort required to implement, modify, and test advanced numerical algorithms. Moreover, the modular design of the code encourages contributions from developers with different levels of expertise and allows for the seamless integration of customized coupled physics solvers and interface solvers. Although GReS is primarily conceived as a prototyping platform, it leverages low-level linear algebra libraries to combine ease of use with fair computational efficiency. In this contribution, we introduce the core concepts underlying GReS and discuss its current state of development, with particular emphasis on its use to implement contact mechanics algorithms for the simulation of fractures, modeled either as explicit lower-dimensional interfaces or as entities embedded within a three-dimensional computational grid. Finally, we illustrate the current platform capabilities through representative model problems relevant to subsurface applications, including aquifer water withdrawal and pore-scale fluid-structure interaction.