交错网格上非均匀三维finite difference弹性波数值模拟
Nonuniform 3D finite difference elastic wave simulation on staggered grids
摘要：
提出了一种在交错网格上采用非均匀有限差分离散的方法来模拟三维各向同性弹性波的传播。具体来说，我们认为模拟域层的均匀网格与不同的网格间距，分离的界面。我们证明，这种逐层有限差分离散化有可能显着降低模拟成本，相比其完全统一的对应。这种离散化的稳定性是通过使用专门设计的差分算子和惩罚项来实现的，所述差分算子是标准差分算子的变体，在边界或界面附近具有自适应性，所述惩罚项被附加到离散化的波系统以弱地施加边界或交界条件。结合特殊设计的插值算子，离散波系统保持了连续弹性波方程的能量守恒性质，$\textit{a fortiori}$保证了模拟的稳定性。数值例子来证明所提出的模拟方法的有效性。
英文摘要：
We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulation domains composed of layers of uniform grids with different grid spacings, separated by nonconforming interfaces. We demonstrate that this layer-wise finite difference discretization has the potential to significantly reduce the simulation cost, compared to its fully uniform counterpart. Stability of such a discretization is achieved by using specially designed difference operators, which are variants of the standard difference operators with adaptations near boundaries or interfaces, and penalty terms, which are appended to the discretized wave system to weakly impose boundary or interface conditions. Combined with specially designed interpolation operators, the discretized wave system is shown to preserve the energy conserving property of the continuous elastic wave equation, and $\textit{a fortiori}$ ensure the stability of the simulation. Numerical examples are presented to demonstrate the efficacy of the proposed simulation approach.
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