Unsupervised Mesh Optimization for Improved Numerical Stability of Finite Volume Methods

Speaker: Mohammad Zandsalimy, University of British Columbia
August 17, 2023

Presentation

Abstract

This work prototypes novel methods to enhance the efficiency of a CFD stability improvement approach based on mesh modification. The problematic parts of the unstructured mesh are identified using the unstable eigenvectors and a few vertices are selected for adjustment. The improved vertex selection methodology ensures a fast and reliable optimization procedure. Movement vectors are calculated using the gradients of unstable eigenmodes with respect to the movement of the selected vertices. A novel approach is presented to remediate the opposing eigenmodes in larger problems. Further, the feasibility of Principal Component Analysis for unstable solution mode identification is studied. After sufficient growth, instabilities appear as anomalies in the dominant numerical modes. Such outliers can be readily detected using standard classification algorithms. The new approach results in complete automation of the mesh optimization application. Furthermore, synthetic vectors are constructed from the unstable solution modes to simulate the behavior of the right eigenvectors which removes the need for eigenanalysis. The results show the feasibility of this novel approach for the stability improvement of finite volume simulations.

Biography

Mohammad Zandsalimy is a Ph.D. candidate in Mechanical Engineering at the University of British Columbia, Vancouver, BC working with Prof. Carl Ollivier-Gooch. His main area of research is the stability analysis and improvement of large-scale Computational Fluid Dynamics. Currently, he is working on mesh optimization for improved stability and convergence rate of finite-volume methods through Eigenanalysis of the semi discrete Jacobian matrix and Principal Component Analysis of solution vectors. He is employing different Machine Learning pipelines to prototype methods for computational cost reduction of the presented optimization algorithms.

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