Graduation Semester and Year

Spring 2025

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Dr. Chaoqun Liu

Abstract

Abstract

LIUTEX-BASED SUBGRID MODEL FOR LARGE EDDY SIMULATION (LES)

Emran Hossen

The University of Texas at Arlington, 2025

Supervising Professor: Dr. Chaoqun Liu

Large Eddy Simulation (LES) is a numerical method in Computational Fluid Dynamics (CFD) designed to simulate turbulent flows more efficiently than traditional approaches. It is important to find a proper subgrid-scale model that is consistent with the underlying physics. Smagorinsky sub-grid model is a popular and classical model for LES, which in general overestimates the eddy viscosity near the wall surface and creates a large discrepancy with direct numerical simulation (DNS) and experiment results. Liutex is a groundbreaking physical quantity, offering scalar, vector, and tensor forms that revolutionized turbulent flow characterization. A Liutex-based SGS model is applied in this research study to do the LES for the channel flow, flat plate boundary transition and backward step flow. Liutex is a vortex identification method, which can correctly represent the flow rotation or vortex. Eddy is vortex; therefore, eddy can be measured by Liutex accurately. Liutex sub-grid model can represent eddy viscosity more properly and accurately. From the computations, the Liutex sub-grid model gives zero eddy viscosity in the laminar sublayer- near the wall region. The theoretical analysis also provides that the eddy viscosity estimated by Liutex-based model is zero near the wall surface while that estimated by Smagorinsky is large which is inconsistent to physics. The streamlines, velocity profiles and reattachment lengths for the simulations of backward step flow are also reported. Only Liutex-based model can resolve a third vortex near the step corner and the reattachment length of Liutex-based model is the closest to Le’s DNS result. The result of flat plate boundary transition shows that Liutex-based model is the one closest to DNS. From the channel flow simulation, analysis with Smagorinsky, Liutex SGS gives zero eddy viscosity near the wall, whereas Smagorinsky model overpredicted.

Keywords

Liutex, Vortex, LES, DNS, Sub-grid, Turbulence

Disciplines

Aerodynamics and Fluid Mechanics | Physical Sciences and Mathematics

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