论文标题
三维弹性和孔隙弹性波传播的不连续的Galerkin方法：前后问题
A Discontinuous Galerkin method for three-dimensional elastic and poroelastic wave propagation: forward and adjoint problems
论文作者
论文摘要
我们基于高阶不连续的Galerkin（DG）方法，开发了用于三维波传播的数值求解器，其用Biot Porolastic波方程式作为一阶保守速度/应变多性增压系统。为了得出上风数值通量，我们找到了对Riemann问题的精确解决方案，包括毛弹性弹性界面；我们还考虑了Biot低频和高频制度中的衰减机制。根据问题的刚度，使用低存储显式或隐式解释（IMEX）runge-kutta方案，我们研究了所提出的DG方案的收敛性能并验证其数值准确性。在Biot低频情况下，对于小渗透率，波浪可能是高度耗散的。在这里，与耗散术语相关的数值错误似乎占主导地位是由主要双曲系统离散化引起的。 然后，我们实施了这种表述的伴随方法。与Biot方程的通常的二阶公式相反，我们不是在处理自动化系统系统，而是使用适当的内部产品，可以通过非保守速度/Biot方程的不保守速度/应力公式来识别伴随。我们为伴随而得出双重通量，并提供了一个简单但启发性的示例。
We develop a numerical solver for three-dimensional wave propagation in coupled poroelastic-elastic media, 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, including the poroelastic-elastic interface; 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.
