声学/ Biot 介质中的波传播：一种有限差分方法
Wave propagation across acoustic / Biot's media: a finite-difference method
AI总结：
针对二维流体/孔隙弹性介质中的波传播问题，开发了结合高阶ADER格式、时空网格细化和浸入界面方法的数值方法，并验证了三种界面条件下的准确性。
摘要：
开发了数值方法以模拟二维非均匀流体/孔隙弹性介质中的波传播。波传播由通常的声学方程（在流体介质中）和低频Biot方程（在孔隙介质中）描述。引入界面条件以模拟两种介质之间的各种水力接触：开孔、密封孔和不完美孔。证明了初边值问题的适定性。先前在孔隙非均匀介质中开发的笛卡尔网格数值方法被适应当前情境：使用Strang分裂的四阶ADER格式进行时间推进；时空网格细化以捕获Biot理论预测的慢压缩波；以及浸入界面方法以离散界面条件并引入亚网格分辨率。针对三种界面条件进行了数值实验并与精确解比较，证明了方法的准确性。
英文摘要：
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-possedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time-marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot's theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach.
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