A solid-fluid boundary condition for the lattice Boltzmann (LB) method, which retains the simplicity of the bounce-back method and leads to positive definite populations similar to the diffusive boundary condition, is presented. As a refill algorithm, it is proposed that quasi-equilibrium distributions be used to model distributions at fluid nodes uncovered due to solid movement. The method is tested for flow past an impulsively started cylinder and demonstrates considerable enhancement in the accuracy of the unsteady force calculation at moderate and high Reynolds numbers. Furthermore, via simulations, we show that momentum exchange procedure used in LB to compute forces is not Galilean invariant. A modified momentum exchange procedure is proposed to reduce the errors due to violation of Galilean invariance.

We show that for the lattice Boltzmann model, the existing paradigm in computer science for the choice of the data structure is suboptimal. In this paper we use the requirements of physical symmetry necessary for recovering hydrodynamics in the lattice Boltzmann description to propose a hybrid data layout for the method. This hybrid data structure, which we call a structure of an array of structures, is shown to be optimal for the lattice Boltzmann model. Finally, the possible advantages of establishing a connection between group theoretic symmetry requirements and the construction of the data structure is discussed in the broader context of grid-based methods.

Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows.

In this paper, we highlight the benefits resulting from imposing energy-conserving equilibria in entropic lattice Boltzmann models for isothermal flows. The advantages are documented through a series of numerical simulations, such as Taylor-Green vortices, cavity flow and flow past a sphere.