Solving elastodynamics in a fluid-solid heterogeneous sphere: a parallel spectral element approximation on non-conforming grids
Solving elastodynamics in a fluid-solid heterogeneous sphere: a parallel spectral element approximation on non-conforming grids
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DOI：
10.1016/s0021-9991(03)00119-0
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发表时间：
2003-05
影响因子：
4.1
通讯作者：
E. Chaljub;Y. Capdeville;J. Vilotte
中科院分区：
文献类型：
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作者：
E. Chaljub;Y. Capdeville;J. Vilotte
我们提出了一种谱元方法来模拟弹性波在固体-流体球体中的传播，其中考虑了重力的局部效应。用固体中的位移和中性分层流体中的速度势对方程进行离散化。空间近似是基于六面体的球面网格，其中局部细化允许在固体和流体区域适应弹性参数的变化离散化。通过拉格朗日乘子引入非协调界面上的连续性约束，并用砂浆单元法将其进一步离散化。由于非协调界面的球形性质，砂浆方法在功能上是协调一致的，并允许对原始变量和拉格朗日乘子进行等阶插值。与弹性参数径向模型的解析计算结果相比，该方法提供了准确的解。它的并行实现基于一种简单的域分解策略，这使得它能够有效地解决像行星尺度那样的大问题。
We present a spectral element approach for modeling elastic wave propagation in a solid–fluid sphere where the local effects of gravity are taken into account. The equations are discretized in terms of the displacement in the solid and the velocity potential in a neutrally stratified fluid. The spatial approximation is based upon a spherical mesh of hexahedra in which local refinement allows for adapting the discretization to the variation of elastic parameters in both the solid and the fluid regions. Continuity constraints across the non-conforming interfaces are introduced through Lagrange multipliers which are further discretized by the mortar element method. Due to the spherical nature of the non-conforming interfaces the mortar method turns out to be functionally conforming and allows for an equal-order interpolation of the primal variables and the Lagrange multipliers. The method is shown to provide an accurate solution when compared to analytical calculations obtained for radial models of elastic parameters. Its parallel implementation is based upon a simple domain decomposition strategy which makes it efficient to solve large problems as those imposed by planetary scales.