论文标题
关于二厘米和物理的内部产品对POD-Galerkin和最小二乘模型的影响，可压缩流的影响
On the impact of dimensionally-consistent and physics-based inner products for POD-Galerkin and least-squares model reduction of compressible flows
论文作者
论文摘要
基于适当的正交分解（POD）和Galerkin正交性或最小二乘的残留最小化基于可压缩欧拉方程的模型降低需要选择内部产品空间，以执行投影并测量规范。最受欢迎的选择是矢量值L2（ω）内部产品空间。但是，这种选择产生了尺寸不足的缩小阶模型（ROM）配方，通常缺乏健壮性。在这项工作中，我们试图通过研究一组具有可压缩欧拉方程的尺寸一致的内部产品来解决这一弱点。首先，我们证明了非二维内部产品对POD和Galerkin/最小二乘ROM都有积极的影响。 Second, we further demonstrate that physics-based inner products based on entropy principles result in drastically more accurate and robust ROM formulations than those based on non-dimensional L2(Ω) inner products.As test cases, we consider the following well-known problems: the one-dimensional Sod shock tube, the two-dimensional Kelvin-Helmholtz instability and two-dimensional homogeneous isotropic turbulence.
Model reduction of the compressible Euler equations based on proper orthogonal decomposition (POD) and Galerkin orthogonality or least-squares residual minimization requires the selection of inner product spaces in which to perform projections and measure norms. The most popular choice is the vector-valued L2(Ω) inner product space. This choice, however, yields dimensionally-inconsistent reduced-order model (ROM) formulations which often lack robustness. In this work, we try to address this weakness by studying a set of dimensionally-consistent inner products with application to the compressible Euler equations. First, we demonstrate that non-dimensional inner products have a positive impact on both POD and Galerkin/least-squares ROMs. Second, we further demonstrate that physics-based inner products based on entropy principles result in drastically more accurate and robust ROM formulations than those based on non-dimensional L2(Ω) inner products.As test cases, we consider the following well-known problems: the one-dimensional Sod shock tube, the two-dimensional Kelvin-Helmholtz instability and two-dimensional homogeneous isotropic turbulence.
