多孔弹性波方程的多尺度波场模拟

本文研究了二维多孔弹性波方程的多尺度波场数值模拟方法.该多尺度方法可采用较粗的网格计算,同时又能反映细尺度上物性参数的变化信息.文中详细阐述了多尺度模拟方法与算法,并推导了相应的计算格式.基本思想是建立粗细两套网格,在粗网格上,基于有限体积方法计算更新波场;在细网格上,计算多尺度基函数,这基于有限元方法通过求解一个局部化问题得到.对含有随机分布散射体的多孔介质模型进行了数值计算,计算中应用了完全匹配层(PML)吸收边界条件,数值结果验证了本文方法和算法的正确性和有效性.

Wave simulation for the poroelastic wave equations by the multiscale method

In this paper, a multiscale method of wave simulation for solving two-dimensional poroelastic wave equations numerically is developed. The multiscale method allows us to apply coarser grids in computations while the information of physical parameter variations in small scale still can be captured. In this paper, the theoretical method and algorithm of the multiscale method are expounded in detail. The corresponding computational schemes are also derived. The basic idea is to construct two sets of meshes, i.e., coarse grids and fine grids. The computations for wavefield updating on coarse grids are implemented based on the finite volume method while the multiscale basis functions are computed on fine grids with the finite element method by solving a local problem. Numerical computations with the perfectly matched layer (PML) absorbing boundary conditions are implemented for a poroelastic model with randomly distributed scatterers and the numerical results verify the correctness and effectiveness of the method and algorithm in this paper.