Partitioned analysis of acoustic fluid–solid-saturated porous medium interaction problems by a generalized saturated porous medium model and localized Lagrange multipliers

Abstract

A partitioned formulation of acoustic fluid–solid-saturated porous medium interaction problems is presented based on a generalized saturated porous medium (GSPM) model and a new localized Lagrange multiplier (LLM) method. In this formula, all various media are modeled as the GSPM and a novel, powerful continuous condition is proposed for the interaction interfaces. This condition applies not only to interfaces of two partitions but also to intersections of simultaneous interactions of any number of media with different porosities. A (u, p) frame is introduced between partitions and the LLM fields are used to connect partitions with the frame. Furthermore, finite element spatial discretization and time integration strategies are provided for both matching meshes and nonmatching meshes. This partitioned formulation is validated numerically by computing the dynamic response of a horizontally layered seawater-seabed-bedrock model subjected to plane waves. The application scenarios for this method include, but are not limited to, the dynamic coupling analysis of marine engineering structures and hydraulic engineering structures. Future work will present and discuss a set of benchmarks and applications that involve the responses of existing dams to seismic excitation.