A hybrid variational-collocation immersed method for fluid-structure interaction using unstructured T-splines
A hybrid variational-collocation immersed method for fluid-structure interaction using unstructured T-splines
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DOI：
10.1002/nme.5004
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发表时间：
2016-03-16
影响因子：
2.9
通讯作者：
Gomez, Hector
中科院分区：
文献类型：
--
作者：
Casquero, Hugo;Liu, Lei;Gomez, Hector
我们提出了一种使用非结构化 T 样条的混合变分搭配、浸入式和完全隐式的流固耦合 (FSI) 公式。在我们的浸入式方法中，我们在整个计算域上定义欧拉网格，在实体域上定义拉格朗日网格，拉格朗日网格在欧拉网格的顶部任意移动。从数学上讲，该问题简化为求解三个方程，即线性动量平衡、质量守恒以及拉格朗日位移和欧拉速度之间的运动相容条件。我们对线性动量和质量守恒方程使用加权残差方法，但我们直接离散化运动学关系的强形式，得出混合变分配置方法。我们使用 T 样条进行空间离散化以及欧拉网格和拉格朗日网格之间的信息传递。与非均匀有理 B 样条相比，T 样条为我们提供了两个主要优势：它们可以进行局部细化并且它们是非结构化的。时间离散化采用广义方法。我们用常见的 FSI 基准问题验证了我们的公式，与理论解决方案取得了极好的一致性。还解决了涉及部分浸入固体的示例。数值示例展示了如何使用 T 形接头和特殊节点来实现准确、高效和灵活的方法。版权所有 (c) 2015 约翰·威利父子有限公司
We present a hybrid variational-collocation, immersed, and fully-implicit formulation for fluid-structure interaction (FSI) using unstructured T-splines. In our immersed methodology, we define an Eulerian mesh on the whole computational domain and a Lagrangian mesh on the solid domain, which moves arbitrarily on top of the Eulerian mesh. Mathematically, the problem reduces to solving three equations, namely, the linear momentum balance, mass conservation, and a condition of kinematic compatibility between the Lagrangian displacement and the Eulerian velocity. We use a weighted residual approach for the linear momentum and mass conservation equations, but we discretize directly the strong form of the kinematic relation, deriving a hybrid variational-collocation method. We use T-splines for both the spatial discretization and the information transfer between the Eulerian mesh and the Lagrangian mesh. T-splines offer us two main advantages against non-uniform rational B-splines: they can be locally refined and they are unstructured. The generalized- method is used for the time discretization. We validate our formulation with a common FSI benchmark problem achieving excellent agreement with the theoretical solution. An example involving a partially immersed solid is also solved. The numerical examples show how the use of T-junctions and extraordinary nodes results in an accurate, efficient, and flexible method. Copyright (c) 2015 John Wiley & Sons, Ltd.