individual
What campus are you from?
Daytona Beach
Authors' Class Standing
Michael Derderian, Senior
Lead Presenter's Name
Michael Derderian
Faculty Mentor Name
Leitao Chen
Abstract
The Lattice Boltzmann Method (LBM) is an increasingly popular alternative to the Navier-Stokes equations due to its simplicity, scalability, and ease of parallel computing. However, single-relaxation-time formulation, known as the lattice Bhatnagar–Gross–Krook (LBGK) model, suffers from numerical instability at high Reynolds numbers where nonphysical negative particle distribution functions can arise. To address this limitation, a Lyapunov H-function can be added that mimics the second law of thermodynamics. This work uses the Essentially Entropic Lattice Boltzmann Method (ELBM) in which this H-function is estimated analytically in the collision term. This provides an enhanced numerical stability without significantly increasing computational cost. A GPU-accelerated CUDA framework is developed to compare the performance, accuracy, and stability of the LBGK and Essentially ELBM solvers. Both the Taylor-Green vortex as well as lid driven cavity flow are used as benchmarks to evaluate the stability and accuracy across a range of Reynolds numbers and grid resolutions. Preliminary results confirm that the Essentially ELBM method achieves improved stability at lower viscosity while maintaining high computational efficiency verifying this as a potential method for extending LBM to higher Reynolds number regimes relevant to turbulent modeling.
Did this research project receive funding support from the Office of Undergraduate Research.
No
Stability Analysis of the Essentially Entropic Lattice-Boltzmann Method for High Reynolds Number Turbulent Flows
The Lattice Boltzmann Method (LBM) is an increasingly popular alternative to the Navier-Stokes equations due to its simplicity, scalability, and ease of parallel computing. However, single-relaxation-time formulation, known as the lattice Bhatnagar–Gross–Krook (LBGK) model, suffers from numerical instability at high Reynolds numbers where nonphysical negative particle distribution functions can arise. To address this limitation, a Lyapunov H-function can be added that mimics the second law of thermodynamics. This work uses the Essentially Entropic Lattice Boltzmann Method (ELBM) in which this H-function is estimated analytically in the collision term. This provides an enhanced numerical stability without significantly increasing computational cost. A GPU-accelerated CUDA framework is developed to compare the performance, accuracy, and stability of the LBGK and Essentially ELBM solvers. Both the Taylor-Green vortex as well as lid driven cavity flow are used as benchmarks to evaluate the stability and accuracy across a range of Reynolds numbers and grid resolutions. Preliminary results confirm that the Essentially ELBM method achieves improved stability at lower viscosity while maintaining high computational efficiency verifying this as a potential method for extending LBM to higher Reynolds number regimes relevant to turbulent modeling.