Entropic multi-relaxation time lattice Boltzmann model for complex flows

Abstract

Entropic lattice Boltzmann methods were introduced to overcome the stability issues of lattice Boltzmann models for high Reynolds number turbulent flows. However, to date their validity has been investigated only for simple flows due to the lack of appropriate boundary conditions. We present here an extension of these models to complex flows involving curved and moving boundaries in three dimensions. Apart from a thorough investigation of resolved and under-resolved simulations for periodic flow and turbulent flow in a round pipe, we study in detail the set-up of a simplified internal combustion engine with a valve/piston arrangement. This arrangement allows us to probe the non-trivial interactions between various flow features such as jet breakup, jet–wall interaction, and formation and breakup of large vortical structures, among others. Besides an order of magnitude reduction in computational costs, when compared to state-of-the-art direct numerical simulations (DNS), these methods come with the additional advantage of using static Cartesian meshes also for moving objects, which reduces the complexity of the scheme. Going beyond first-order statistics, a detailed comparison of mean and root-mean-square velocity profiles with high-order spectral element DNS simulations and experimental data shows excellent agreement, highlighting the accuracy and reliability of the method for resolved simulations. Moreover, we show that the implicit subgrid features of the entropic lattice Boltzmann method can be utilized to further reduce the grid sizes and the computational costs, providing an alternative to modern modelling approaches such as large-eddy simulations for complex flows.

Entropic multirelaxation-time lattice Boltzmann method for moving and deforming geometries in three dimensions

“…Recently, the entropic concept was extended to multi-relaxation time models (KBC models), where the additional freedom of multiple relaxation parameters is used to keep the effective viscosity at its nominal value while retaining stability. Excellent performance of KBC models in terms of stability and accuracy for under-resolved simulations have been reported in the works of Bösch et al [5], Dorschner et al [12], Karlin et al [26]. Due to its advantages, all simulations in the remainder of the paper are conducted using the KBC model.…”

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Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work Dorschner et al [11] as well as for three dimensional one-way coupled simulations of engine-type geometries in Dorschner et al [12] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases including two-way coupling between fluid and structure, turbulence and deformable meshes.

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Grid refinement for entropic lattice Boltzmann models

“…In contrast to other MRT models, the KBC suggests that the rate at which those moments should be relaxed is determined by maximizing the entropy. The derivation of KBC models was already discussed in our previous publications [8,10,11]; here we remind the main steps. Let us recall the set of natural moments of the D3Q27 lattice given by…”

A numerical tool for the study of the hydrodynamic recovery of the Lattice Boltzmann Method

“…This tool is based on the systematic calculation of each term of the kinetic energy and enstrophy balance equations averaged over a suitable ensemble of sub-volumes of the computational grid. A similar approach to characterize LBM hydrodynamics was successfully used in [24,25]…”