Essentially entropic lattice Boltzmann model

Abstract

Fluid ows are constitutive to a wide variety of scienti c and engineering problems, owing to the fact that they encompass a vast range of spatial and temporal scales. An accurate prediction of the uid ow has innumerable commercial applications in turbomachinery, petrochemical industries, hydraulic machines, inkjet printing, as well as is of great scienti c interest for multiphase

ows, non-Newtonian ows, hydrodynamic instability and transition to turbulence (Dixon & Hall, 2013; Oliemans, 2012; Batchelor, 2000; Leal, 2007). Fluid dynamics becomes crucial during scenarios that require knowledge of ows over an aortic stenosis, designing arti cial heart valves, and predicting extreme weather patterns such as cyclones, oods, hurricanes. Additionally, a quick prediction of the atmospheric ows can lead to the prior knowledge of the expected rainfall, which will reduce losses in the regions that are dependent on the rain for the purpose of agricultural irrigation. Although seemingly disparate, the various ows in the continuum regime, irrespective of the spatial and temporal scales, are similar and are governed by the Navier-Stokes-Fourier (NSF) equations (Batchelor, 2000). These equations can be simpli ed and solved to obtain a closed form solution for a large class of problems (Leal, 2007). However, they do not render a general solution for many realistic engineering and scienti c problems, particularly in the case of turbulent ows where the nonlinearity of the NSF equations gives rise to chaotic beahviour. One has to, therefore, resort to numerical methods to solve them. The direct numerical simulations (DNS), where all the scales of the ow are resolved, are the most reliable numerical approaches for solving the NSF equations. However, the DNS of many realistic ows such as the turbulent

ows requires grid sizes that are often too large (Pope, 2000). With the existing approaches, it is widely accepted that DNS of turbulent ows will be feasible only after a decade (Thantanapally et al., 2013a; Slotnick et al., 2014; Larsson & Wang, 2014). Thus, one looks for viable alternates to it such as the turbulence models. They reduce the computational load by modeling the subgrid phenomena and projecting it onto a coarse grid. However, the choice of these turbulence model is problem speci c and hence these models lack universality.