A Discontinuous Galerkin Method for Three-Dimensional Poroelastic Wave Propagation: Forward and Adjoint Problems

被引:0
作者
Nick Dudley Ward
Simon Eveson
Timo Lähivaara
机构
[1] Australian National University,Research School of Engineering
[2] University of York,Department of Mathematics
[3] University of Eastern Finland,Department of Applied Physics
来源
Computational Methods and Function Theory | 2021年 / 21卷
关键词
Discontinuous Galerkin method; Poroelastic waves; Adjoint method; 86-08; 35R30;
D O I
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学科分类号
摘要
We develop a numerical solver for three-dimensional poroelastic wave propagation, based on a high-order discontinuous Galerkin (DG) method, with the Biot poroelastic wave equation formulated as a first order conservative velocity/strain hyperbolic system. To derive an upwind numerical flux, we find an exact solution to the Riemann problem; we also consider attenuation mechanisms both in Biot’s low- and high-frequency regimes. Using either a low-storage explicit or implicit–explicit (IMEX) Runge–Kutta scheme, according to the stiffness of the problem, we study the convergence properties of the proposed DG scheme and verify its numerical accuracy. In the Biot low frequency case, the wave can be highly dissipative for small permeabilities; here, numerical errors associated with the dissipation terms appear to dominate those arising from discretisation of the main hyperbolic system. We then implement the adjoint method for this formulation of Biot’s equation. In contrast with the usual second order formulation of the Biot equation, we are not dealing with a self-adjoint system but, with an appropriate inner product, the adjoint may be identified with a non-conservative velocity/stress formulation of the Biot equation. We derive dual fluxes for the adjoint and present a simple but illuminating example of the application of the adjoint method.
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页码:737 / 777
页数:40
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