Residual vector and solution mode analysis using semi-supervised machine learning for mesh modification and CFD stability improvement

Abstract

Novel methods are studied to improve the performance of our previous mesh optimization approach for the stability improvement of unstructured-mesh finite-volume simulations. The residual vector as well as solution modes from Principal Component Analysis of solution vectors is analyzed for this purpose. After sufficient growth, instabilities appear as anomalies in the dominant numerical modes. Using standard classification algorithms, such outliers can be detected readily and much more efficiently compared to the eigenanalysis of the Jacobian matrix, which was required by the forebears of the current study. Further, it is essential to identify the correct local regions on the mesh for possible modification of vertex location and to remove the noise from the non-related cells. Hence, a synthetic vector is constructed from the working vector containing instabilities to simulate the behavior of the right eigenvectors in the solution. The results show the feasibility of residual vector analysis and principal component analysis of solution vectors for the stability improvement of finite-volume simulations. The new approach results in complete automation of the mesh optimization application.