Three-Dimensional Mapped-Grid Finite Volume Modeling of Poroelastic-Fluid Wave Propagation

TL;DR

This paper develops a high-resolution finite volume model for simulating wave propagation in three-dimensional poroelastic-fluid systems using mapped grids, introducing a novel limiting algorithm and verifying its accuracy through various tests.

Contribution

It presents a new 3D finite volume method with a compatible limiting algorithm for anisotropic media on non-rectilinear grids, extending previous 2D work.

Findings

The new limiter reduces solution error in anisotropic media.

The code accurately simulates wave propagation in complex geological settings.

Verification against plane wave solutions confirms the method's correctness.

Abstract

This paper extends the author's previous two-dimensional work with Ou and LeVeque to high-resolution finite volume modeling of systems of fluids and poroelastic media in three dimensions, using logically rectangular mapped grids. A method is described for calculating consistent cell face areas and normal vectors for a finite volume method on a general non-rectilinear hexahedral grid. A novel limiting algorithm is also developed to cope with difficulties encountered in implementing high-resolution finite volume methods for anisotropic media on non-rectilinear grids; the new limiting approach is compatible with any limiter function, and typically reduces solution error even in situations where it is not necessary for correct functioning of the numerical method. Dimensional splitting is used to reduce the computational cost of the solution. The code implementing the three-dimensional algorithms is verified against known plane wave solutions, with particular attention to the performance of the new limiter algorithm in comparison to the classical one. An acoustic wave in brine striking an uneven bed of orthotropic layered sandstone is also simulated in order to demonstrate the capabilities of the simulation code.