Accurate Calculation of Fault-Rupture Models Using the High-Order Discontinuous Galerkin Method on Tetrahedral Meshes
Accurate Calculation of Fault-Rupture Models Using the High-Order Discontinuous Galerkin Method on Tetrahedral Meshes
复制标题
四面体网格高阶间断伽辽金法精确计算断层破裂模型
DOI：
10.1785/0120060253
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发表时间：
2007
影响因子：
3
通讯作者：
M. Dumbser
中科院分区：
文献类型：
--
作者：
M. Käser;P. Mai;M. Dumbser
我们提出了一种新的方法，近源地面运动的计算，由于地震破裂的潜在几何复杂的断层。继最近推出的间断Galerkin方法与当地时间步进四面体网格，我们使用分段多项式近似的未知变量内的每个元素，并实现相同的逼近阶在时间和空间，由于新的ader时间积分方案，使用任意高阶导数。我们展示了如何一个外部源项及其在空间和时间上的异质性，给出了一个扩展的破裂面的精细离散化，可以包括在更粗的四面体网格由于子单元分辨率的高阶多项式表示。因此，破裂表面非常一般地表示为各个子断层的中心位置的点云，在该点云处，每个多项式测试函数在单元内被精确地评估，并且源项的时空积分在每个时间步长处被精确地计算。除了将复杂的震源运动学，我们还提出了模型边界的影响，可以降低地震记录的准确性，由于弱人工反射。我们提出了一个扩展的计算域的粗网格缓冲区，并表明，我们的计划使用本地时间步长完全避免了这样的边界问题，只有稍微增加计算成本。我们验证了新的方法对不同的测试用例，比较我们的结果与分析，准分析，和一系列的参考解决方案。我们的工作表明，添加功能，准确地处理有限的源破裂模型的ader-Discontinuous Galerkin方法的一般框架是一个重要的贡献，模拟现实的地震场景，允许有效地列入异构源运动学和复杂的破裂面几何形状在近源地面运动模拟。
We present a new method for near-source ground-motion calculations due to earthquake rupture on potentially geometrically complex faults. Following the recently introduced Discontinuous Galerkin approach with local time stepping on tetrahedral meshes, we use piecewise polynomial approximations of the unknown variables inside each element and achieve the same approximation order in time and space due to the new ader time integration scheme that uses Arbitrary high-order DERivatives. We show how an external source term and its heterogeneous properties in space and time, given by a fine discretization of an extended rupture surface, can be included in much coarser tetrahedral meshes due to the subcell resolution of the high-order polynomial representation. Hereby, the rupture surface is represented very generally as a point cloud of the center locations of individual subfaults at which each polynomial test function is evaluated exactly inside an element and the space– time integration of the source term is accurately computed at each timestep. Besides the incorporation of complex source kinematics we also present the effects of model boundaries that can degrade the accuracy of seismograms due to weak artificial reflections. We propose an extended computational domain of a coarsely meshed buffer region and show that our scheme using the local timestepping completely avoids such boundary problems with only slightly increasing the computational cost. We validate the new approach against different test cases, comparing our results with analytic, quasianalytic, and a series of reference solutions. Our work shows that adding the functionality of accurately treating finite source-rupture models into the general framework of the ader-Discontinuous Galerkin approach is an important contribution to modeling realistic earthquake scenarios, allowing the efficient inclusion of heterogeneous source kinematics and complex rupture-surface geometries in near-source ground-motion simulations.