Unsupervised Residual Vector Analysis for Mesh Optimization

This work prototypes novel methods to enhance the efficiency of a previous CFD stability improvement approach. The feasibility of residual vector analysis for unstable solution mode identification is studied. Unsupervised machine learning models in the form of outlier detectors are used to identify anomalous vector elements. A novel method is presented to construct synthetic vectors that resemble unstable eigenvectors. Synthetic vectors are used to find vertices for modification and calculate the vertex movement direction and magnitude. The residual vector helps substantially in reducing the computational cost of the optimization algorithm. In comparison to the full eigenanalysis of the Jacobian matrix, residual vector analysis requires much fewer computational resources. This methodology is used for the first time for the stability improvement of finite-volume simulations. It is shown that using residual vector analysis for the identification of the unstable solution modes and problematic cells in the mesh has a similar stabilization performance to using the right eigenvectors.