Modeling Wave Propagation in a Coupled System of Elastic Solid and Viscous Fluid Using Graphical Processing Units (GPUs)

Abstract Accurate characterization of complex geophysical environments requires both appropriate governing equations and robust numerical modeling techniques. This is particularly critical in media that are not purely elastic solids, but are saturated with viscous fluids. We present a novel numerical scheme for simulating wave propagation in a coupled solid–fluid system. The solid phase is modeled as a linear elastic medium using the momentum balance equation and Hooke’s law. The fluid phase is governed by the compressible Navier–Stokes equations. A unified numerical framework is developed to consistently couple the two domains. We provide a rigorous analysis of the governing equations, including dimensional analysis, dispersion analysis, and von Neumann stability analysis. The numerical solver is validated against exact analytical solutions. We further benchmark the full 3D coupled system using full waveform modeling in a fluid-filled borehole, demonstrating excellent agreement with semi-analytical solutions. We implement the solver on a single GPU, achieving performance close to the hardware limit, and report a speedup of up to two orders of magnitude compared to CPU-based implementations for high-resolution models exceeding 260 million voxels. The proposed methodology enables efficient simulation of wave propagation in coupled solid–fluid systems, capturing the influence of fluid viscosity on acoustic responses. The framework can be applied to investigate the effect of localized fluid flow in fractured borehole environment and squirt-flow mechanisms at pore scale.