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Stability Analysis and Improvement in Computational Fluid Dynamics

AMS Seminar Series

Speaker: Mohammad Zandsalimy, The University of British Columbia

Presentation

Seminar Slide Deck (PDF-10.7MB)

Abstract

A novel method for enhancing the numerical stability of computational simulations via mesh optimization is introduced. This technique employs Dynamic Mode Decomposition to approximate the evolution of non-linear solutions as a linear mapping, effectively reducing the system’s degrees of freedom. Through eigenanalysis of the reduced system, the growth rates and oscillation frequencies of the dominant solution modes are determined. Key control volumes and vertices influencing these dynamic modes are then identified. By computing the gradients of the Jacobian diagonal elements with respect to the movement of these vertices, their positions are adjusted to enhance the diagonal dominance of the corresponding Jacobian rows. The method is validated using both an in-house flow solver and Ansys Fluent, demonstrating its flexibility and non-invasive nature requiring no modifications or access to the host solver’s source code. Compared to existing techniques, this approach significantly reduces computational costs while improving numerical stability. Extensive results highlight the robustness and effectiveness of this advanced mesh optimization strategy.

Biography

Photo of Mohammad Zandsalimy
Mohammad Zandsalimy is a skilled researcher in computational science, specializing in the stability analysis and enhancement of large-scale computational simulations. He earned his Ph.D. in Mechanical Engineering from the University of British Columbia in 2024, working with Prof. Carl Ollivier-Gooch. During his doctoral studies, Zandsalimy focused on advancing numerical stability in computational models, particularly through innovative approaches such as Dynamic Mode Decomposition of solution update vectors. His groundbreaking work includes the development of novel mesh optimization techniques, which have significantly improved the accuracy and efficiency of computational simulations. Zandsalimy is currently seeking opportunities to apply his expertise in computational science to real-world industrial problems.