Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics
Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics
复制标题
用于 ALE 流体动力学中重新映射的张量量的保界重建
DOI：
10.1007/978-3-319-91548-7_11
复制
发表时间：
2016
影响因子：
15
通讯作者：
J. Velechovský
中科院分区：
文献类型：
--
作者：
Matěj Klíma;M. Kucharik;M. Shashkov;J. Velechovský
在ALE弹性流数值模拟中，我们分析了几种新的和现有的在偏应力重映射的背景下限制张量的方法。张量逐分量的重新映射和限制被证明违反了衍生变量（如弹性能量或力）的径向对称性。因此，我们扩展了对称保持矢量图像多边形算法，最初是为限制矢量变量而设计的。这个限制器将向量（在我们的例子中是一个独立张量分量的向量）限制在由周围单元的向量构成的凸包内——这相当于标量变量中的离散极大值原理。我们将这种方法与专为偏应力限制而设计的限制器进行比较，偏应力限制器旨在约束与比弹性能量成正比的\(J_2\)不变量并相应地缩放张量。我们还提出了一种使用已知标量技术独立地重新映射和限制\(J_2\)不变量的方法。然后对偏应力张量进行缩放以匹配这个重新映射的不变量，这保证了弹性能量方面的守恒。
We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component are shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells—an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the \(J_2\) invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the \(J_2\) invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.