瞬态二维粘弹性波的数值模拟
Numerical modeling of transient two-dimensional viscoelastic waves
AI总结：
本文采用广义Zener模型描述线性粘弹性固体中的耗散机制，通过引入记忆变量避免时间卷积，并利用分裂方法（显式四阶ADER格式与精确求解扩散部分）结合浸入界面法离散界面跳跃条件，实现了瞬态机械波的高效数值模拟。
摘要：
本文研究线性粘弹性固体中瞬态机械波的数值模拟。耗散机制采用广义Zener模型描述。通过引入满足局部时间微分方程的记忆变量，无需时间卷积。通过适当选择松弛参数，可以精确描述多种材料，例如具有恒定品质因数的固体。速度、应力和记忆变量满足的演化方程写为带有源项的一阶偏微分方程组。通过将该系统分裂为两部分求解：传播部分采用笛卡尔网格上的四阶ADER格式显式离散，扩散部分则精确求解。界面处的跳跃条件采用浸入界面法离散。在粘弹性和流体介质中的波传播数值实验表明，该数值模型能有效处理诸如多重散射构型等挑战性问题。
英文摘要：
This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the generalized Zener model. No time convolutions are required thanks to the introduction of memory variables that satisfy local-in-time differential equations. By appropriately choosing the relaxation parameters, it is possible to accurately describe a large range of materials, such as solids with constant quality factors. The evolution equations satisfied by the velocity, the stress, and the memory variables are written in the form of a first-order system of PDEs with a source term. This system is solved by splitting it into two parts: the propagative part is discretized explicitly, using a fourth-order ADER scheme on a Cartesian grid, and the diffusive part is then solved exactly. Jump conditions along the interfaces are discretized by applying an immersed interface method. Numerical experiments of wave propagation in viscoelastic and fluid media show the efficiency of this numerical modeling for dealing with challenging problems, such as multiple scattering configurations.
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