Abstract

A finite-difference approximation of elastic forces on Lagrangian grids is constructed by applying the support operator method. For displacement vectors on unstructured grids with minimal reasonable constraints imposed on their topological and geometric structure, approximations of vector analysis operations are constructed as applied to difference schemes for elasticity problems. Taking into account the energy balance of the medium, the constructed families of integrally consistent approximations of vector analysis operations are sufficient for discrete simulation of these processes. Schemes are considered in which the stress tensor is used in explicit form or is split into a spherical and a shear component (pressure and deviator). The latter approach is used to construct uniform algorithms applicable to both the solid body and the evaporated phase. The approximations are constructed using linear elasticity theory. The resulting forces are obtained in explicit form in three-dimensional geometry. Sound waves propagating in a three-dimensional orthogonal aluminum plate as generated by an impact on its end are computed.

中文翻译：

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一种求解具有弹性过程容限的三维流体动力学问题的方法

摘要

拉格朗日网格上弹性力的有限差分近似是通过应用支持算子方法构建的。对于在拓扑和几何结构上施加最小合理约束的非结构化网格上的位移向量，构建了向量分析操作的近似值，以应用于弹性问题的差分方案。考虑到介质的能量平衡，向量分析操作的整体一致近似的构造族足以用于这些过程的离散模拟。考虑以显式形式使用应力张量或将其拆分为球形和剪切分量（压力和偏差）的方案。后一种方法用于构建适用于固体和蒸发相的统一算法。近似值是使用线性弹性理论构建的。所产生的力在三维几何中以明确的形式获得。计算在 3D 正交铝板中传播的声波，因为它的末端受到撞击而产生。