Isogeometric Analysis for Explicit Wave Propagation in Poroelastic Media
Please login to view abstract download link
Extraction of natural gas in the north of the Netherlands has induced seismicity, in an area that was formerly stable. To better understand the potential hazards resulting from future subsurface activities, such as geothermal energy production or underground CO2 storage, numerical modeling of seismic wave propagation is of interest. One area that demands special attention is the shallow subsurface. When a seismic wave transitions from stiff earth into softer, uncompacted soils that are characteristic near the surface, it increases in amplitude. Thus, capturing this region is essential for hazard assessment. However, accurately modeling this region is challenging. The resolution of the model should be sufficient to capture the variety in soil types. In addition, uncompacted soil is not represented well by elasticity theory. Instead, we intend to model it as poroelastic. Despite these challenges, computational effort must remain limited to allow for stochastic simulations at scale. To accomplish this, Isogeometric Analysis (IGA) is a promising discretization method. It enables higher-order discretizations without inflating the number of degrees of freedom. In addition, when employing FEM, the critical timestep in an explicit time integration scheme is reduced as the order of the method is increased. This decrease is lessened using IGA [1]. If outlier frequencies are eliminated as well, the critical timestep becomes essentially independent of the order [2]. Thus, one of the major downsides of higher-order methods in explicit dynamics may be eliminated. These results have been established in the context of elasticity. In our study, we extend these results to poroelasticity. By analyzing discrete spectra, we investigate how the critical timestep depends on the discretization method. In addition, we compare two formulations of poroelasticity theory. References [1] J.A. Cottrell, A. Reali, Y. Bazilevs, T.J.R. Hughes, Isogeometric analysis of structural vibrations. Computer Methods in Applied Mechanics and Engineering, 195(41-43)., 5257-5296., 2006. [2] R.R. Hiemstra, T.J.R. Hughes, A. Reali, D. Schillinger., Removal of spurious outlier frequencies and modes from isogeometric discretizations of second-and fourth-order problems in one, two, and three dimensions, Computer Methods in Applied Mechanics and Engineering, 387., 114115., 2021
