An a priori reduced order method based on the proper generalised decomposition (PGD) is proposed to compute parametric solutions involving turbulent incompressible flows of interest in an industrial context, using OpenFOAM. The PGD framework is applied for the first time to the incompressible Navier-Stokes equations in the turbulent regime, to compute a generalised solution for velocity, pressure and turbulent viscosity, explicitly depending on the design parameters of the problem. In order to simulate flows of industrial interest, a minimally intrusive implementation based on OpenFOAM SIMPLE algorithm applied to the Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model is devised. The resulting PGD strategy is applied to parametric flow control problems and achieves both qualitative and quantitative agreement with the full order OpenFOAM solution for convection-dominated fully-developed turbulent incompressible flows, with Reynolds number up to one million.

中文翻译：

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OpenFOAM 中湍流不可压缩流动的参数解通过适当的广义分解

提出了一种基于适当广义分解 (PGD) 的先验降阶方法，以使用 OpenFOAM 计算涉及工业环境中感兴趣的湍流不可压缩流动的参数解。PGD​​ 框架首次应用于湍流状态中的不可压缩 Navier-Stokes 方程，以计算速度、压力和湍流粘度的广义解，明确取决于问题的设计参数。为了模拟工业利益流，设计了一种基于 OpenFOAM SIMPLE 算法的最小侵入实现，该算法应用于具有 Spalart-Allmaras 湍流模型的 Reynolds 平均 Navier-Stokes 方程。