论文标题
交错网格上的不均匀3D有限差弹性波模拟
Nonuniform 3D finite difference elastic wave simulation on staggered grids
论文作者
论文摘要
我们提出了一种使用交错网格上的有限差异化离散化，模拟3D各向同性弹性波的传播。具体而言，我们考虑由具有不同网格间距的均匀网格层组成的仿真域，并由不合格的接口隔开。我们证明，与完全均匀的对应物相比，这种有限的有限差离散化有可能显着降低模拟成本。这种离散化的稳定性是通过使用特殊设计的差异运算符来实现的，这些差异操作员是标准差异操作员的变体，并在边界或接口附近进行适应，而惩罚条款则附加到离散的波浪系统上，以弱强加于边界或接口条件。结合专门设计的插值操作员，已证明离散的波系统可保留连续弹性波方程的能量保存特性，$ \ textit {a fortiori} $确保模拟的稳定性。提出了数值示例，以证明所提出的仿真方法的功效。
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.
