We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

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A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives accurate results over a wide range of Reynolds numbers. Studies of errors and convergence rates are carried out. Compressibility effects are quantified for different maximum velocities, and parameter ranges are found for stable simulations. The paper's objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers.

The JHU turbulence database [1] can be used with a state of the art visualisation tool [2] to generate high quality fluid dynamics videos. In this work we investigate the classical idea that smaller structures in turbulent flows, while engaged in their own internal dynamics, are advected by the larger structures. They are not advected undistorted, however. We see instead that the small scale structures are sheared and twisted by the larger scales. This illuminates the basic mechanisms of the turbulent cascade. THE JHU TURBULENCE DATABASEIn [1] a database containing a solution of the 3D incompressible Navier-Stokes (NS) equations is presented. The equations were solved numerically with a standard pseudo-spectral simulation in a periodic domain, using a real space grid of 1024 3 grid points. A large-scale body force drives a turbulent flow with a Taylor microscale based Reynolds number R λ = 433. Out of this solution, 1024 snapshots were stored, spread out evenly over a large eddy turnover time. More on the simulation and on accessing the data can be found at http://turbulence.pha.jhu.edu. In practical terms, we have easy access to the turbulent velocity field and pressure at every point in space and time. VORTICES WITHIN VORTICESOne usual way of visualising a turbulent velocity field is to plot vorticity isosurfaces -see for instance the plots from [3]. The resulting pictures are usually very "crowded", in the sense that there are many intertwined thin vortex tubes, generating an extremely complex structure. In fact, the picture of the entire dataset from [3] looks extremely noisy and it is arguably not very informative about the turbulent dynamics.In this work, we follow a different approach. First of all, we use the alternate quantityfirst introduced in [4]. Secondly, the tool being used has the option of displaying data only inside clearly defined domains of 3D space. We can exploit this facility to investigate the multiscale character of the turbulent cascade. Because vorticity is dominated by the smallest available scales in the velocity, we can visualize vorticity at scale ℓ by the curl of the velocity box-filtered at scale ℓ. We follow a simple procedure:• we filter the velocity field, using a box filter of size ℓ 1 , and we generate semitransparent surfaces delimitating the domains D 1 where Q > q 1 ;• we filter the velocity field, using a box filter of size ℓ 2 < ℓ 1 , and we generate surfaces delimitating the domains D 2 where Q ≥ q 2 , but only if these domains are contained in one of the domains from D 1 ;and this procedure can be used iteratively with several scales (we use at most 3 scales, since the images become too complex for more levels). Additionally, we wish sometimes to keep track of the relative orientation of the vorticity vectors at the different scales. For this purpose we employ a special coloring scheme for the Q isosurfaces: for each point of the surface, we compute the cosine of the angle α between the ℓ 2 filtered vorticity and the ℓ 1 filtered vorticity: cos α = (∇ × u 1 ) · (∇ × u ...

We propose the viscous Camassa-Holm equations as a closure approximation for the Reynoldsaveraged equations of the incompressible Navier-Stokes fluid. This approximation is tested on turbulent channel flows with steady mean. Analytical solutions for the mean velocity and the Reynolds shear stress across the entire channel are obtained, showing good agreement with experimental measurements and direct numerical simulations. As Reynolds number varies, these analytical mean velocity profiles form a family of curves whose envelopes are shown to have either power law, or logarithmic behavior, depending on the choice of drag law.

A hybrid multiscale method is developed for simulating micro-and nano-scale fluid flows. The continuum Navier-Stokes equation is used in one flow region and atomistic molecular dynamics in another. The spatial coupling between continuum equations and molecular dynamics is achieved through constrained dynamics in an overlap region. The proposed multiscale method is used to simulate sudden-start Couette flow and channel flow with nano-scale rough walls, showing quantitative agreement with results from analytical solutions and full molecular dynamics simulations for different parameter regimes. Potential applications of the proposed multiscale method are discussed.

We introduce a lattice Boltzmann computational scheme capable of modeling ther-