论文标题
基于投影的不稳定压缩流的校准模型
Calibration of projection-based reduced-order models for unsteady compressible flows
论文作者
论文摘要
在这项工作中介绍了减少阶模型（ROM）的校准分析。在涉及时间尺度差异的可压缩流中测试了Galerkin和最小二乘Petrov-Galerkin（LSPG）方法。提出了针对LSPG方法的新型校准策略，并分析了两个测试用例。第一个由亚音速翼型流量组成，其中边界层不稳定性负责落后噪声的产生，第二个则包括超音速式机翼流，其瞬态周期是脱节的冲击波在同一时间传播了冲击涡流相互作用在尾随边缘。结果表明，校准在两种情况下均可产生稳定且长期准确。为了降低LSPG模型的计算成本，采用了加速的贪婪缺失点估计（MPE）算法进行过度还原。对于第一个调查的情况，通过超重还原获得的LSPG溶液与完整订单模型获得的LSPG溶液进行了良好的比较。但是，对于超音速案例，流量的瞬态特征需要由采样点正确捕获。否则，移动冲击波的动力学将无法完全恢复。还评估了不同时间级方案的影响，并且与文献中报道的不同，盖尔金模型与在求解Navier-Stokes方程的非保守形式时所计算出的盖尔金模型更准确。对于超音速案例，Galerkin和LSPG模型（不进行过度还原）捕获了沿机翼的分离和倾斜冲击波的整体动力学。但是，当冲击 - 涡流相互作用发生在尾随边缘时，Galerkin ROM能够捕获涡流脱落中的高频波动，而LSPG提出了更耗散的解决方案，无法恢复流动动力学。
An analysis of calibration for reduced-order models (ROMs) is presented in this work. The Galerkin and least-squares Petrov-Galerkin (LSPG) methods are tested on compressible flows involving a disparity of temporal scales. A novel calibration strategy is proposed for the LSPG method and two test cases are analyzed. The first consists of a subsonic airfoil flow where boundary layer instabilities are responsible for trailing-edge noise generation and the second comprises a supersonic airfoil flow with a transient period where a detached shock wave propagates upstream at the same time that shock-vortex interaction occurs at the trailing edge. Results show that calibration produces stable and long-time accurate for both cases. In order to reduce the computational costs of the LSPG models, an accelerated greedy missing point estimation (MPE) algorithm is employed for hyper-reduction. For the first case investigated, LSPG solutions obtained with hyper-reduction show good comparison with those obtained by the full order model. However, for the supersonic case the transient features of the flow need to be properly captured by the sampled points. Otherwise, the dynamics of the moving shock wave are not fully recovered. The impact of different time-marching schemes is also assessed and, differently than reported in literature, Galerkin models are shown to be more accurate than those computed by LSPG when the non-conservative form of the Navier-Stokes equations are solved. For the supersonic case, the Galerkin and LSPG models (without hyper-reduction) capture the overall dynamics of the detached and oblique shock waves along the airfoil. However, when shock-vortex interaction occurs at the trailing-edge, the Galerkin ROM is able to capture the high-frequency fluctuations from vortex shedding while the LSPG presents a more dissipative solution, not being able to recover the flow dynamics.
