Title : Recent Advancements in Numerical Methods for Subsurface Simulations
Abstract:In this talk, I will present a collection of recent advancements in solving multi-physics coupled systems in porous media. These include physics-preserving finite element methods, phase-field fracture approach, reduced-order modeling techniques, approaches to inverse problems using DeepONet, and methods for optimal control problems. First, it is essential to develop computationally robust and physics-preserving numerical methods that eliminate spurious oscillations, ensuring accurate and stable simulations of the underlying physical processes. These methods are especially important in the context of multi-physics systems, where interactions between different physical phenomena must be accurately captured. Secondly, there is growing interest in solving inverse problems in porous media to infer unknown physical parameters of the system. By utilizing DeepONet, a neural operator framework, we can efficiently solve these inverse problems, which are critical for applications such as groundwater modeling and geo-energy simulations. Finally, optimal control problems, which aim to optimize system behavior under given constraints, are increasingly applied in subsurface simulations, enabling better management and control of resources.