Finite Volume Modeling of Poroelastic-Fluid Wave Propagation with Mapped Grids

TL;DR

This paper presents a high-resolution finite volume method on mapped grids for simulating wave propagation in complex poroelastic and fluid media with curved interfaces, verified against analytical solutions and applied to biological tissue modeling.

Contribution

It introduces a unified formulation for interface conditions and a modified Riemann solver within the Clawpack framework for accurate wave modeling across media boundaries.

Findings

Achieved second-order convergence at flat interfaces in 1-norm.

Demonstrated code capability with realistic biological tissue simulation.

Validated the method against analytical solutions for wave reflection and scattering.

Abstract

In this work we develop a high-resolution mapped-grid finite volume method code to model wave propagation in two dimensions in systems of multiple orthotropic poroelastic media and/or fluids, with curved interfaces between different media. We use a unified formulation to simplify modeling of the various interface conditions -- open pores, imperfect hydraulic contact, or sealed pores -- that may exist between such media. Our numerical code is based on the Clawpack framework, but in order to obtain correct results at a material interface we use a modified transverse Riemann solution scheme, and at such interfaces are forced to drop the second-order correction term typical of high-resolution finite volume methods. We verify our code against analytical solutions for reflection and transmission of waves at a material interface, and for scattering of an acoustic wave train around an isotropic poroelastic cylinder. For reflection and transmission at a flat interface, we achieve second-order convergence in the 1-norm, and first-order in the max-norm; for the cylindrical scatterer, the highly distorted grid mapping degrades performance but we still achieve convergence at a reduced rate. We also simulate an acoustic pulse striking a simplified model of a human femur bone, as an example of the capabilities of the code. To aid in reproducibility, at the web site http://dx.doi.org/10.6084/m9.figshare.701483 we provide all of the code used to generate the results here.