Implementation and verification of LES models for SRT Lattice Boltzmann methods.

Abstract

In the last two decades, the Lattice Boltzmann Method (LBM) has experienced tremendous progress and rise in its application by academia and industry. This fact has led to the development of a variety of LBM solvers, both commercial and academic. Two critical factors for this success are its inexpensive numerical step and parallel scalability compared to more mainstream approaches, such as Finite Volume Navier-Stokes solvers. The main target of this project is the introduction and testing of LES models into the academic solver AMROC, developed currently at the University of Southampton. The three LES models to be considered are Constant and Dynamic Smagorinsky (CSMA & DSMA) and WALE.Initially, three wall-free test cases, namely Forced and Decaying Homogeneous Isotropic Turbulence (FHIT & DHIT) and the Taylor-Green Vortex (TGV), were employed to verify the algorithms of the new implementations. To further improve the understanding of the models and their inter-coupling with LBM, besides the Standard (STA) Single Relaxation Time (SRT) collision model, I have also used the Regularised (REG) collision model for comparative analysis. Simultaneously, I have also investigated the effect of calculating the strain rate locally, using the non-equilibrium part, or through a finite difference stencil. An abundance of valuable data and conclusions has been obtained. The next step was the simulation of the bi-periodic turbulent channel. In this scenario, I have validated the LES models by capturing the law of the wall. A new algorithm for imposing macrovariables in ghost cells where bounce-back-like boundary conditions are applied has been devised in parallel. This capability is of utmost importance for the LES models, particularly DSMA and WALE, in which the calculation of the eddy viscosity is based on a stencil. Therefore its calculation is possible in the first fluid cell. To further improve the ability of the solver to deal with high Re flows, a wall function has also been implemented and tested using the bi-periodic channel case. The final test case was a square cylinder on a flat plate at an angle of 90o. This case aimed to verify the wall function for a body not aligned to the Cartesian mesh.

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ORCID for Ralf Deiterding: orcid.org/0000-0003-4776-8183

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