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首页> 外文期刊>Journal of Computational Physics >Stable Galerkin reduced order models for linearized compressible flow
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Stable Galerkin reduced order models for linearized compressible flow

机译：线性压缩流的稳定Galerkin降阶模型

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The Galerkin projection procedure for construction of reduced order models of compressible flow is examined as an alternative discretization of the governing differential equations. The numerical stability of Galerkin models is shown to depend on the choice of inner product for the projection. For the linearized Euler equations, a symmetry transformation leads to a stable formulation for the inner product. Boundary conditions for compressible flow that preserve stability of the reduced order model are constructed. Preservation of stability for the discrete implementation of the Galerkin projection is made possible using a piecewise-smooth finite element basis. Stability of the reduced order model using this approach is demonstrated on several model problems, where a suitable approximation basis is generated using proper orthogonal decomposition of a transient computational fluid dynamics simulation. (C) 2008 Elsevier Inc. All rights reserved.
机译：构造可压缩流降阶模型的Galerkin投影程序作为控制微分方程的另一种离散化方法进行了研究。结果表明，Galerkin模型的数值稳定性取决于投影的内积选择。对于线性化的Euler方程，对称变换可得出内积的稳定公式。构造了可压缩流的边界条件，该边界条件保留了降阶模型的稳定性。使用分段平滑的有限元基础，可以为Galerkin投影的离散实现保留稳定性。在几个模型问题上证明了使用这种方法的降阶模型的稳定性，其中使用瞬态计算流体动力学模拟的适当正交分解生成了合适的近似基础。 （C）2008 Elsevier Inc.保留所有权利。

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