SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids
SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids
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DOI：
10.1016/j.cam.2018.08.040
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发表时间：
2018-02
期刊：
影响因子：
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通讯作者：
Longfei Gao;D. C. D. R. Fernández-D.-C.-D.-R.-Fernández-145704654;M. Carpenter;D. Keyes
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文献类型：
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作者：
Longfei Gao;D. C. D. R. Fernández-D.-C.-D.-R.-Fernández-145704654;M. Carpenter;D. Keyes
我们考虑了地震应用中的声波方程的数值模拟，交错网格有限差分方法由于其简单和高效而成为流行的选择。我们放宽了对有限差分方法的均匀网格限制，允许网格具有非协调界面的分块均匀网格。通过这样做，可以更有效地解释地下介质波速的变化。设计了满足分块求和(SBP)性质的交错网格有限差分算子来逼近声波方程中的空间导数。这些运算符在每个块中独立应用。块之间的耦合是通过同时逼近项(SAT)实现的，它对界面条件施加较弱的影响，即通过惩罚来实现。允许相邻块的网格间距之比为有理数，并给出了专门设计的插补公式。这些内插公式构成了同时逼近项的关键部分。整个离散化被证明是节能的，并在理论和实际感兴趣的测试用例上进行了检验，提供了准确和稳定的模拟结果。
We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface conditions weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.