论文标题
通过第四阶有限差法，曲线坐标中曲面坐标的弹性波传播
Elastic wave propagation in curvilinear coordinates with mesh refinement interfaces by a fourth order finite difference method
论文作者
论文摘要
我们为具有分段光滑材料特性的各向同性介质中的三维弹性波方程开发了第四阶准确的有限差方法。在我们的模型中，材料特性在弯曲接口处可能是不连续的。通过使用第四阶有限差算子满足逐个属性的求和属性的第四阶有限差算子，以曲线网格的二阶形式离散。该方法是能量稳定且高阶准确的。重点是，可以根据材料的速度结构选择网格尺寸，从而提高计算效率。在带有悬挂节点的网格改进接口处，通过使用幽灵点和插值来施加物理接口条件。使用第四阶预测器 - 校正时间集成器，完全离散的方案是能源保存的。提出了数值实验，以验证第四阶收敛速率和能源保存特性。
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved interfaces. The governing equations are discretized in second order form on curvilinear meshes by using a fourth order finite difference operator satisfying a summation-by-parts property. The method is energy stable and high order accurate. The highlight is that mesh sizes can be chosen according to the velocity structure of the material so that computational efficiency is improved. At the mesh refinement interfaces with hanging nodes, physical interface conditions are imposed by using ghost points and interpolation. With a fourth order predictor-corrector time integrator, the fully discrete scheme is energy conserving. Numerical experiments are presented to verify the fourth order convergence rate and the energy conserving property.
