A Unified Numerical Scheme for Coupled Multiphysics Model
Yijie Zhang, Haixia Zhao, Wenjing Yan, Jinghuai Gao
Abstract
For oil and gas exploration, seismic wave propagation in coupled acoustic, elastic, poroelastic, and even anisotropic media is a valuable aspect. However, it is a challenging task to deal with the interfaces of the coupled model. In order to tackle the specific issue, a unified numerical scheme is developed, which is based on the discontinuous Galerkin method. The acoustic, elastic, poroelastic, and anisotropic elastic wave equations are unified into a first-order velocity–stress system. The numerical simulation at the interfaces in the coupled model is conveniently handled by the Godunov flux without any extra operations. Numerical results from the coupled acoustic–elastic and acoustic–poroelastic model are compared with the analytic solutions. In addition, the rates of convergence from different orders are analyzed, which demonstrates the accuracy of the proposed numerical scheme. The surface waves at the fluid–solid interface are studied. Moreover, the proposed scheme is applied to a more complex coupled model, including the coupled acoustic–elastic–poroelastic model and the coupled acoustic–anisotropic elastic model. The corresponding results demonstrate that the proposed numerical scheme is capable of dealing with the coupled model.