Global/local model order reduction in coupled flow and linear thermal-poroelasticity

Abstract

Coupled flow and geomechanics computations are very complex and require solving large nonlinear systems. Such simulations are intense from both runtime and memory standpoint, which strongly hints at employing model order reduction (MOR) techniques to speed them up. Different types of Reduced-Order Models (ROM) have been proposed to alleviate this computational burden. MOR approaches rely on projection operators to decrease the dimensionality of the problem. We first execute a computationally expensive “offline” stage, during which we carefully study the full order model (FOM). Upon creating a ROM basis, we then perform the cheap “online” stage. Our reduction strategy estimates a ROM using proper orthogonal decomposition (POD). We determine a family of solutions to the problem, for a suitable sample of input conditions, where every single realization is so-called a “snapshot.” We then ensemble all snapshots to determine a compressed subspace that spans the solution. Usually, POD employs a fixed reduced subspace of global basis vectors. The usage of a global basis is not convenient to tackle problems characterized by different physical regimes, parameter changes, or high-frequency features. Having many snapshots to capture all these variations is unfeasible, which suggests seeking adaptive approaches based on the closest regional basis. We thus develop such a strategy based on local POD basis to reduce one-way coupled flow and geomechanics computations. We partition the time window to adequately capture regimes such as depletion/build-up and decreasing the number of snapshots per basis. We focus on linear elasticity and consider factors such as the role of the heterogeneity. We also assess how to tackle different degrees of freedom, such as the displacements (intercalated and coupled), pressure, and temperature, with MOR. Preliminary 2- and 3-D results show significant compression ratios up to 99.9% for the mechanics part. We formally compare FOM and ROM and provide time data to demonstrate the speedup of the procedure. Examples focus on linear and nonlinear poroelasticity. We employ continuous Galerkin finite elements for all of the discretizations.