A Spectral Element Reduced Basis Method for Navier–Stokes Equations with Geometric Variations
A Spectral Element Reduced Basis Method for Navier–Stokes Equations with Geometric Variations
复制标题
具有几何变分的纳维-斯托克斯方程的谱元简化基法
DOI：
10.1007/978-3-030-39647-3_45
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
G. Rozza
中科院分区：
文献类型：
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作者：
M. Hess;A. Quaini;G. Rozza
我们考虑具有变高度缩窄的通道中的Navier-Stokes方程。模型采用高阶谱元ANSATZ函数离散，得到6372个自由度。稳态快照解决方案通过标准POD程序定义了减少的订单空间。降阶空间可以准确、高效地计算不同几何形状的稳态解。特别是，我们详细描述了结合谱元素离散化实现降阶模型的不同方面。结果表明，在参数多查询场景中，单元局部自由度的扩展可以与降阶建模方法相结合来提高计算时间。
We consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions define a reduced order space through a standard POD procedure. The reduced order space allows to accurately and efficiently evaluate the steady-state solutions for different geometries. In particular, we detail different aspects of implementing the reduced order model in combination with a spectral element discretization. It is shown that an expansion in element-wise local degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.