论文标题
有效的基于正交分解的有效降低阶模型
An Efficient Proper Orthogonal Decomposition based Reduced-Order Model
论文作者
论文摘要
本文提出了一种基于可压缩流的新型，更有效的基于更有效的正交分解（POD）的还原阶模型（ROM）。在此POD模型中，使用特定体积而不是密度编写了质量，动量和能量方程的控制方程，即质量，动量和能量方程式。这种替换允许构成降低阶模型的ODES系数的预发行。采用了几种方法来增强ODE求解器的稳定性：强制边界条件，人工耗散的惩罚方法以及一种修改POD近似模式数量的方法。这种新的基于POD的还原模型已在四种情况下在转录条件下进行了验证：一个准二维喷嘴，二维通道，三维轴对称喷嘴和透视风扇。在所有测试的情况下，使用基于POD的ROM与全阶模型获得的加速度均超过四个数量级。
This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy equations were written using specific volume instead of density. This substitution allowed for the pre-computation of the coefficients of the system of ODEs that make up the reduced-order model. Several methods were employed to enhance the stability of the ODE solver: the penalty method to enforce boundary conditions, artificial dissipation, and a method that modifies the number of modes used in the POD approximation. This new POD-based reduced-order model was validated for four cases at both on- and off-reference conditions: a quasi-one-dimensional nozzle, a two-dimensional channel, a three-dimensional axisymmetric nozzle, and a transonic fan. The speedup obtained by using the POD-based ROM vs. the full-order model exceeded four orders of magnitude in all cases tested.
