Resolving wave propagation in anisotropic poroelastic media using
graphical processing units (GPUs)
- Yury Alkhimenkov,
- Ludovic Räss,
- Lyudmila Khakimova,
- Beatriz Quintal,
- Yury Podladchikov
Abstract
Biot's equations describe the physics of hydro-mechanically coupled
systems establishing the widely recognized theory of poroelasticity.
This theory has a broad range of applications in Earth and biological
sciences as well as in engineering. The numerical solution of Biot's
equations is challenging because wave propagation and fluid pressure
diffusion processes occur simultaneously but feature very different
characteristic time scales. Analogous to geophysical data acquisition,
high resolution and three dimensional numerical experiments lately
re-defined state of the art. Tackling high spatial and temporal
resolution requires a high-performance computing approach. We developed
a multi-GPU numerical application to resolve the anisotropic
elastodynamic Biot's equations that relies on a conservative numerical
scheme to simulate, in a few seconds, wave fields for spatial domains
involving more than 1.5 billion grid cells. We present a comprehensive
dimensional analysis reducing the number of material parameters needed
for the numerical experiments from ten to four. Furthermore, the
dimensional analysis emphasizes the key material parameters governing
the physics of wave propagation in poroelastic media. We perform a
dispersion analysis as function of dimensionless parameters leading to
simple and transparent dispersion relations. We then benchmark our
numerical solution against an analytical plane wave solution. Finally,
we present several numerical modeling experiments, including a
three-dimensional simulation of fluid injection into a poroelastic
medium. We provide the Matlab, symbolic Maple, and GPU CUDA C routines
to reproduce the main presented results. The high efficiency of our
numerical implementation makes it readily usable to investigate
three-dimensional and high-resolution scenarios of practical
applications.Jul 2021Published in Journal of Geophysical Research: Solid Earth volume 126 issue 7. 10.1029/2020JB021175