Interaction of Waves with Frictional Interfaces Using Summation-by-Parts Difference Operators: Weak Enforcement of Nonlinear Boundary Conditions
Interaction of Waves with Frictional Interfaces Using Summation-by-Parts Difference Operators: Weak Enforcement of Nonlinear Boundary Conditions
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DOI：
10.1007/s10915-011-9485-3
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发表时间：
2012-02-01
影响因子：
2.5
通讯作者：
Nordstrom, Jan
中科院分区：
文献类型：
--
作者：
Kozdon, Jeremy E.;Dunham, Eric M.;Nordstrom, Jan
本文提出了一种高阶差分方法来求解弹性动力学中的波与高度非线性摩擦界面的相互作用问题。我们限制我们的注意力二维反平面问题只涉及一个方向的变形。将界面或断层上的牵引力与其上的相对滑动速度联系起来的跳跃条件，其形式与地震破裂模型和其他摩擦滑动问题中使用的形式密切相关。通过使用部分求和（SBP）有限差分算子和弱的边界条件和界面条件，严格稳定的方法。此外，它表明，除非非线性界面条件制定的特征变量，而不是物理变量，他们是更自然地表示，半离散系统的方程可以变得非常僵硬，防止有效的解决方案，使用显式时间integrators.The使用SBP运营商也提供了一个严格定义的能量平衡的离散化问题，随着网格的细化，接近连续问题中的精确能量平衡。这使人们能够研究地震能量学，例如，在破裂过程中释放的弹性应变能转换为地震波携带的辐射能，而不是通过断层的摩擦滑动耗散的效率。这些理论结果证实了在一个和两个维度的计算效率，高阶收敛速度的方法，使用严格稳定的数值方法进行长时间积分的好处，和能量平衡的准确性的几个数值试验。
We present a high-order difference method for problems in elastodynamics involving the interaction of waves with highly nonlinear frictional interfaces. We restrict our attention to two-dimensional antiplane problems involving deformation in only one direction. Jump conditions that relate tractions on the interface, or fault, to the relative sliding velocity across it are of a form closely related to those used in earthquake rupture models and other frictional sliding problems. By using summation-by-parts (SBP) finite difference operators and weak enforcement of boundary and interface conditions, a strictly stable method is developed. Furthermore, it is shown that unless the nonlinear interface conditions are formulated in terms of characteristic variables, as opposed to the physical variables in terms of which they are more naturally stated, the semi-discretized system of equations can become extremely stiff, preventing efficient solution using explicit time integrators.The use of SBP operators also provides a rigorously defined energy balance for the discretized problem that, as the mesh is refined, approaches the exact energy balance in the continuous problem. This enables one to investigate earthquake energetics, for example the efficiency with which elastic strain energy released during rupture is converted to radiated energy carried by seismic waves, rather than dissipated by frictional sliding of the fault. These theoretical results are confirmed by several numerical tests in both one and two dimensions demonstrating the computational efficiency, the high-order convergence rate of the method, the benefits of using strictly stable numerical methods for long time integration, and the accuracy of the energy balance.