A novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Model-discovery and cross-validation is performed for three cases of separating flows, i.e. periodic hills ( R e =10595), converging-diverging channel ( R e =12600) and curved backward-facing step ( R e =13700). The predictions of the discovered models are significantly improved over the k - ω SST also for a true prediction of the flow over periodic hills at R e =37000. This study shows a systematic assessment of SpaRTA for rapid machine-learning of robust corrections for standard RANS turbulence models.

中文翻译：

---

使用稀疏符号回归发现代数雷诺应力模型

引入了一种新的确定性符号回归方法 SpaARTA（湍流应力各向异性的稀疏回归），以直接从高保真 LES 或 DNS 数据推断代数应力模型，用于 RANS 方程的闭合。这些模型被写成张量多项式，并从候选函数库中构建。机器学习方法基于弹性网络正则化，可提高推断模型的稀疏性。通过数据驱动，该方法放宽了模型开发过程中常见的假设。模型发现和交叉验证对三种分离流情况进行，即周期性山丘（R e =10595）、收敛-发散通道（R e =12600）和弯曲向后台阶（R e =13700）。所发现模型的预测在 k - ω SST 上也得到了显着改善，也可以真实预测 Re = 37000 处周期性山丘上的流量。这项研究显示了对 SpaARTA 的系统评估，用于快速机器学习标准 RANS 湍流模型的稳健校正。