(535i) Optimized Turbulence Modeling Via Lattice Boltzmann Method

Sesha Hari Vemuri, Yu Liu, Pil Seung Chung, Myung S. Jhon, and Lorenz T. Biegler

Numerical simulation of turbulent flow is a challenging subject with a long history where there are many conceptual and numerical difficulties associated with analyzing various fluid flow characteristics occurring at high Reynolds number. To model turbulence phenomena, there have been numerous approaches including additional parameters and equations to describe the flow of eddies. This results in a number of uncertainties in the input from heuristically motivated artificial model parameters. These additional equations in modeling this flow, constituting the so-called turbulence models with higher degrees of freedom (i.e., two equation models), typically involve certain parameters which can be justified only heuristically from empirical information and experimental data. The adjustment of these turbulence parameters is often not obvious, guided principally by “what worked before,” even if the model is now used in a different application. Thus, an important question in the CFD community now is how the results of the overall simulation depend on the turbulence parameters, where if the results are strongly affected by these parameters, the uncertainty of the simulation is considered to be high.

Since the last two decades, and alternative flexible methodologies such as lattice Boltzmann method (LBM) are increasingly popular to describe experimental findings as well as offer advantages of algorithmic simplicity, transient nature, easiness in the treatment of complex geometrical boundaries and amenability to parallel computing platform. In this work, we attempt to explore in developing an optimized LBM solver to examine the turbulent flow around bluff bodies and other complex geometries using multiple turbulence models including large eddy simulation with Smagorinsky sub-grid model, k-e, RNG k-e, and k-w models and compare our simulation result with experimental data. To improve our numerical result, we introduce a cost function based on the means square difference between the simulation result and experimental data, and adapt control theory to the lattice Boltzmann equation and obtained  the model sensitivity, which results into the optimized adjoint lattice Boltzmann equation[1]. To verify our optimized LBM, we consider two scenarios: a simple Poiseuille flow, and a complex turbulence modeling. Our optimized model illustrated robust convergence behavior for both examples and was able to generate accurate relaxation parameter estimates efficiently.

[1] M.M. Tekitek , M. Bouzidi , F. Dubois , P. Lallemand, Comput. Fluids 35 805 (2006).