Modares Mechanical Engineering

Modares Mechanical Engineering

Numerical Stability Enhancement of Lattice Boltzmann Method in The Simulation of Incompressible Flows with Higher Reynolds Numbers

Document Type : Original Research

Authors
Mohammad Reza Saremi Tehrani 1
Mohsen Ghadyani 1
Vali Enjilela 2
1 Islamic Azad University, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch
2 Islamic Azad University, Karaj Branch
10.22034/MME.24.3.177
Abstract
In this study, a new upwind scheme has been used to solve the continuous Boltzmann equation and to develop its application in the effective solution of incompressible flows. Time derivative in the Boltzmann equation has been discretized using the first-order forward finite difference scheme. The spatial derivatives in the Boltzmann equation have been discretized using this new scheme. Further, the combined effects of the upwind differential mechanism along with the finite difference method are presented to enhancement the stability of the standard lattice Boltzmann method in solving problems with high Reynolds numbers. To confirm the validation of the proposed method, one unsteady problem, this has an analytical solution, and two incompressible steady problems which have not analytical solutions, have been solved numerically. The first benchmark problem is the conductive heat transfer on a slab and two last problems are flow over a flat plate and flow in a lid-driven cavity. In order to check the numerical accuracy and stability of the proposed method, the results have been compared with the standard lattice Boltzmann method and the finite difference lattice Boltzmann method. The proposed method guarantees that without applying the filtering method, more stable and accurate results are obtained compared with the finite difference lattice Boltzmann method. The simulation results show the effectiveness of the present method and its appropriate compatibility with analytical solutions and other numerical methods.
Keywords
Incompressible Flow
Standard Lattice Boltzmann Method
Finite Difference Lattice Boltzmann Method
Numerical Stability
Upwind Scheme

Subjects

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Modares Mechanical Engineering
Volume 24, Issue 3
February 2024
Pages 177-188