Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions
Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions
复制标题
DOI：
10.1016/j.jcp.2020.109842
复制
发表时间：
2020-03
期刊：
影响因子：
--
通讯作者：
M. Almquist;E. Dunham
中科院分区：
文献类型：
--
作者：
M. Almquist;E. Dunham
分部求和有限差分法对于二阶波动方程具有几个理想的性质。它们将窄模板有限差分算子的计算效率与曲线多块网格上可证明的稳定性相结合。虽然存在几种边界和界面条件的技术，但通过同时逼近项（SATs）进行弱施加可能是最灵活的一种。虽然SBP方法已多次应用于弹性波动方程，但对于一般各向异性弹性波动方程的SBP- sat方法尚未在文献中提出。我们通过在曲线多块网格上推导一般各向异性材料的能量稳定自伴随SBP-SAT方法来填补这一空白。这些方法基于完全兼容的SBP算子。虽然本文的重点是经典的SBP有限差分算子，但所提出的边界和界面处理是一般的，适用于满足SBP性质的一系列方法。我们用制造解的方法证明了一组完全兼容的SBP-SAT方案的稳定性和准确性。我们还演示了新方法在弹性动力隐身和山区地震成像中的实用性。
Summation-by-parts (SBP) finite difference methods have several desirable properties for second-order wave equations. They combine the computational efficiency of narrow-stencil finite difference operators with provable stability on curvilinear multiblock grids. While several techniques for boundary and interface conditions exist, weak imposition via simultaneous approximation terms (SATs) is perhaps the most flexible one. Although SBP methods have been applied to elastic wave equations many times, an SBP-SAT method for general anisotropic elastic wave equations has not yet been presented in the literature. We fill this gap by deriving energy-stable self-adjoint SBP-SAT methods for general anisotropic materials on curvilinear multiblock grids. The methods are based on fully compatible SBP operators. Although this paper focuses on classical SBP finite difference operators, the presented boundary and interface treatments are general and apply to a range of methods that satisfy an SBP property. We demonstrate the stability and accuracy properties of a particular set of fully compatible SBP-SAT schemes using the method of manufactured solutions. We also demonstrate the utility of the new method in elastodynamic cloaking and seismic imaging in mountainous regions.