Finite-Difference modeling of elastic wave propagation in solid-moving fluid systems

Numerical simulations of elastic or acoustic wave propagation usually assume a stationary background medium. In many practical situations, however, such as marine exploration or the inspection of engineered structures pipelines, elastic waves propagate in bodies of moving fluid as well. Ambient flow fields introduce changes to the wave field such as a direction-dependent wave propagation velocity or phase shifts that can be observed in real-world measurements. To obtain simulations that more faithfully represent elastic wave propagation in coupled systems of stationary solids and moving fluids, and that are better suited for comparison with experimental, laboratory, and field data in the future, a formulation is introduced in which a material derivative expands the elastic wave equation. The resulting partial differential equation is solved using an augmented rotated-staggered finite-difference scheme that combines the spatial operators of the rotated-staggered grid with a conventional central-difference approximation. The performance of this new formulation is examined on the propagation of elastic wave fields in ambient steady uniform and steady laminar flow fields in combined fluid-solid models, and compared to reference simulation with no moving background medium. The analysis focuses on travel-time variations and phase shifts, demonstrating that the numerical results are consistent with analytical expectations for wave propagation in moving media.