论文标题
大规模弹性波模拟3D复合几何形状中的大规模弹性波模拟的零件有限差异方法的上风总和
Upwind summation by parts finite difference methods for large scale elastic wave simulations in 3D complex geometries
论文作者
论文摘要
高阶准确列为零件（SBP）有限差（FD）方法构成了模拟大型双曲波传播问题的有效数值方法。传统的SBP FD操作员在其计算的解决方案中近似具有中央差异模具的一阶空间衍生物通常具有虚假未解决的数值波模式。最近，基于上风的FD模板，最近得出的高阶准确的上风SBP运算符具有抑制这些有毒的伪造波模型在边缘分辨的计算网格上。在本文中，我们证明并非所有高级上风SBP FD操作员都适用。数值分散关系分析表明，奇数上风的SBP FD操作员还支持在略有分辨的网格上进行杂散的未解决的高频。同时，均衡的上风SBP FD运算符（第2、4、6阶）不支持虚假未解决的高频波模式，并且具有更好的数值分散属性。我们在边界构造曲线网格上离散三个空间维（3D）弹性波方程。使用能量方法，我们证明了半分化近似是稳定且能量持续的。我们得出先验误差估计，并证明数值误差的收敛性。复杂几何形状中3D弹性波方程的数值实验证实了理论分析。给出了具有复杂非平面游离表面形貌的异质介质中3D弹性波方程的数值模拟，包括对社区开发的地震基准问题的数值模拟。计算结果表明，与奇数级上风和传统的SBP FD运算符相比，均衡的均匀上风SBP FD运算符更有效，更强大且易于降低数值分散误差。
High-order accurate summation-by-parts (SBP) finite difference (FD) methods constitute efficient numerical methods for simulating large-scale hyperbolic wave propagation problems. Traditional SBP FD operators that approximate first-order spatial derivatives with central-difference stencils often have spurious unresolved numerical wave-modes in their computed solutions. Recently derived high order accurate upwind SBP operators based upwind FD stencils have the potential to suppress these poisonous spurious wave-modes on marginally resolved computational grids. In this paper, we demonstrate that not all high order upwind SBP FD operators are applicable. Numerical dispersion relation analysis shows that odd-order upwind SBP FD operators also support spurious unresolved high-frequencies on marginally resolved meshes. Meanwhile, even-order upwind SBP FD operators (of order 2, 4, 6) do not support spurious unresolved high frequency wave modes and also have better numerical dispersion properties. We discretise the three space dimensional (3D) elastic wave equation on boundary-conforming curvilinear meshes. Using the energy method we prove that the semi-discrete approximation is stable and energy-conserving. We derive a priori error estimate and prove the convergence of the numerical error. Numerical experiments for the 3D elastic wave equation in complex geometries corroborate the theoretical analysis. Numerical simulations of the 3D elastic wave equation in heterogeneous media with complex non-planar free surface topography are given, including numerical simulations of community developed seismological benchmark problems. Computational results show that even-order upwind SBP FD operators are more efficient, robust and less prone to numerical dispersion errors on marginally resolved meshes when compared to the odd-order upwind and traditional SBP FD operators.
