Project R-12561

AdaPore: rigorous and fully adaptive model selection for multiphase flow through porous media (Research)

Multiphase flow through heterogeneous porous domains describes processes such as oil and gas extraction, hydrogeological flow, and CO2 sequestration in the subsurface. The porous flow models depend on the number of phases involved and range from linear elliptic to nonlinear degenerate parabolic, hyperbolic, and even higher-order equations if hysteresis and dynamic effects are considered. A choice of model is often made a priori based on experience and computational budget. This project aims to investigate the adaptive selection of accurate and computationally inexpensive mathematical and numerical models locally in space-time subdomains. This will be achieved by deriving locally space-time efficient a-posteriori estimators and other mathematically rigorous error indicators. The sub-problems defined over the subdomains will be solved in parallel and will be combined through a heterogeneous domain decomposition scheme. The convergence of the scheme will be proved and codes will be developed for industrial-scale problems. For the hyperbolic case, non-classical Riemann solutions, resulting from the incorporation of hysteresis and dynamic effects, will be derived and implemented in a Godunov type solver. Machine learning will be used to expedite the selection of sub-domains and non-classical Riemann solutions at mesh interfaces.

01 June 2022 - 31 October 2023