Learning Dominant Physical Processes with Data-Driven Balance Models for Shock-Separated Flows

High fidelity simulations of shock-turbulent boundary layer interactions (STBLI) solve the complex nonlinear governing equations requiring massive computational resources. However, local regions of the flow can often be reduced to a dominant subset of physical processes. Traditionally, simplification of the governing equations to approximate the local dominant physics have relied on analytical methods such as dimensional analysis and asymptotic methods. These approaches are however mathematically cumbersome for complex flows. In this work, the turbulent compressible governing equations for a canonical shock-separated ramp flow are reduced to local dominant subsets using machine learning methods. Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) data are used to generate data-driven models which are used to automatically identify distinct local regions of dominant physics. The method herein uses a Gaussian Mixture Model (GMM) probabilistic framework to cluster the data into dominant balance regions. Each cluster represents a set of active terms that approximates the full governing equations. Sparse Principal Components Analysis (SPCA) is then applied to combine redundant clusters. The resulting automatically identified local dominant balance regions and their physical interpretations are compared with apriori analyses. The prediction accuracy and viability of the method to uncover reduced-order mechanistic models in STBLI flows and for general application to multi-scale, multi-physics flows are discussed.