A Stable Galerkin Reduced Order Model (ROM) for Compressible Flow.
A Stable Galerkin Reduced Order Model (ROM) for Compressible Flow.
复制标题
可压缩流的稳定伽辽金降阶模型（ROM）。
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Arunajatesan
中科院分区：
文献类型：
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作者：
I. Kalashnikova;S. Arunajatesan
描述了一种构造可压缩流动稳定的本征正交分解（POD）/Galerkin降阶模型（ROM）的方法。所提出的模型降阶技术不同于在许多应用中所采取的方法，因为Galerkin投影步骤被应用于偏微分方程（PDE）的连续系统，而不是这些方程的半离散表示。研究表明，用于定义伽辽金投影的内积与所得模型的稳定性密切相关。对于线性化的守恒律，如线性化的可压缩欧拉方程和线性化的可压缩Navier-Stokes方程，对称变换导致内积的稳定公式。保持稳定的离散实施的Galerkin投影是可能的，使用分段光滑的有限元基础，和一个弱的执行边界条件。所提出的模型简化方法的稳定性和准确性进行了研究的背景下，两个测试用例：在一个均匀的底流的无粘压力脉冲的问题，和粘性层流空腔问题。对于第二个固有非线性测试用例，在POD简化基础模式中捕获了流的非线性动态，但在投影到这些模式上的方程中没有捕获，因为ROM方程基于完全非线性流方程的局部线性化。
A method for constructing stable Proper Orthogonal Decomposition (POD)/Galerkin reduced order models (ROMs) for compressible flow is described. The proposed model reduction technique differs from the approach taken in many applications in that the Galerkin projection step is applied to the continuous system of partial differential equations (PDEs), rather than a semi-discrete representation of these equations. It is demonstrated that the inner product used to define the Galerkin projection is intimately tied to the stability of the resulting model. For linearized conservation laws such as the linearized compressible Euler and linearized compressible Navier-Stokes equations, a symmetry transformation leads to a stable formulation for the inner product. Preservation of stability for the discrete implementation of the Galerkin projection is made possible using piecewise-smooth finite element bases, and a weak enforcement of the boundary conditions. The stability and accuracy of the proposed model reduction approach is studied in the context of two test cases: the problem of an inviscid pressure pulse in a uniform base flow, and a viscous laminar cavity problem. For the second inherently non-linear test case, the non-linear dynamics of the flow are captured in the POD reduced basis modes, but not in the equations projected onto these modes, as the ROM equations are based on a local linearization of the full non-linear flow equations.