AIAA SciTech 2024: Dynamic Mode Decomposition For Improved Numerical Stability of Finite Volume Simulations
Date:
Title: Dynamic Mode Decomposition For Improved Numerical Stability of Finite Volume Simulations
Presentation video: Not Available
Speaker: Mohammad Zandsalimy, PhD Candidate, Mechanical Engineering, University of British Columbia
Date: Thursday, January 11, 2024
Time: 09:30 - 09:50 EDT
Location: Celebration 7
Abstract
We propose a novel approach to mesh optimization for improved stability of finite-volume simulations using dynamic mode decomposition on a subset of the solution vectors. A minimal number of the most recent solution vectors in the simulation are selected for dynamic mode decomposition. The eigenvalues of the Koopman matrix depict the magnitude growth rate and oscillation frequency of the largest solution modes. The computational cost of this method depends on the number of solution vectors in use, which is considerably less expensive compared to the eigenanalysis of the full Jacobian matrix. The dynamic eigenvectors are utilized to identify which control volumes and vertices have the greatest impact on each dynamic solution mode. The gradients of the Jacobian matrix diagonal are calculated with respect to the movement of the selected vertices. The positions of these points are adjusted to increase the diagonal dominance of the Jacobian matrix on the corresponding rows. The results verify the effectiveness and feasibility of the novel approach in numerical stability improvement through unstructured mesh optimization. This state-of-the-art method addresses the challenges faced by the latest studies in this field with full automation of the mesh optimization process and substantial computational savings.