We explore the capability of lattice Boltzmann equation (LBE) method for complex fluid flows involving turbulence, mixing, and reaction. In the first study, LBE schemes for binary scalar mixing and multi-component reacting flow with reactions are developed. Simulations of initially non-premixed mixtures yield scalar probability distribution functions that are in good agreement with numerical data obtained from Navier-Stokes (NS) equation based computation. One-dimensional chemically-reacting flow simulation of a premixed mixture yields a flame speed that is consistent with experimentally determined value. The second study involves direct numerical simulation (DNS) and large-eddy simulation (LES) of decaying homogenous isotropic turbulence (HIT) with and without frame rotation. Three categories of simulations are performed: (i) LBE-DNS in both inertial and rotating frames; (ii) LBE-LES in inertial frame; (iii) Comparison of the LBE-LES vs. NS-LES. The LBE-DNS results of the decay exponents for kinetic energy k and dissipation rate ε, and the low wave-number scaling of the energy spectrum agree well with established classical results. The LBE-DNS also captures rotating turbulence physics. The LBE-LES accurately captures low-wave number scaling, energy decay and large scale structures. The comparisons indicate that the LBE-LES simulations preserve flow structures somewhat more accurately than the NS-LES counterpart. In the third study, we numerically investigate the near-field mixing features in low aspect-ratio (AR) rectangular turbulent jets (RTJ) using the LBE method. We use D3Q19 multiple-relaxation-time (MRT) LBE incorporating a subgrid Smagorinsky model for LES. Simulations of four jets which characterized by AR, exit velocity, and Reynolds number are performed. The investigated near-field behaviors include: (1) Decay of mean streamwise velocity (MSV) and inverse MSV; (2) Spanwise and lateral profiles of MSV; (3) Half-velocity width development and MSV contours; and (4) Streamwise turbulence intensity distribution and spanwise profiles of streamwise turbulence intensity. The computations are compared against experimental data and the agreement is good. We capture both unique features of RTJ: the saddle-back spanwise profile of MSV and axis-switching of long axis from spanwise to lateral direction. Overall, this work serves to establish the feasibility of the LBE method as a viable tool for computing mixing, combustion, and turbulence.

Three-dimensional large-eddy simulations (LES) of single and multiple jets in cross-flow (JICF) were conducted using the 19-bit Lattice Boltzmann Equation (LBE) method coupled with a conventional Navier-Stokes (NS) finite-volume scheme. In this coupled LBE-NS approach, the LBE-LES was employed to simulate the flow inside jet nozzles, while the NS-LES was used to simulate the cross-flow. The key application area was to study the micro-blowing technique (MBT) for drag control similar to recent experiments at NASA/GRC. A single jet in the cross-flow case was used for validation purposes, and results were compared with experimental data and full LBE-LES simulation. Good agreement with data was obtained. Transient analysis of flow structures was performed to investigate the contribution of flow structures to the counter-rotating vortex pair (CRVP) formation. It was found that both spanwise roller (at the lee side of the jet) and streamwise vortices (at the jet-side) contribute to the generation of the CRVP. Span-wise roller at the corner of the jet experiences high spanwise vortex compression as well as high streamwise vortex stretch. As a result, they get realigned, mix with the jet-side streamwise vortices, and eventually generate the CRVP. Furthermore, acoustic pulses were used to test the proper information exchange from the LBE domain to the NS domain, and vice-versa. Subsequently, MBT over a flat plate with porosity of 25 percent was simulated using nine jets in a compressible cross-flow at a Mach number of 0.4. Three cases with injection ratios of 0.003, 0.02 and 0.07 were conducted to investigate how the blowing rate impacts skin friction. It is shown that MBT suppressed the near-wall vortices and reduced the skin friction by up to 50 percent. This is in good agreement with experimental data.

<p> Working within the framework of the linearized Boltzmann equation for the conduction electrons the existing theoretical treatments of ultrasonic attenuation in metals are extended to include realistic descriptions of the electronic structure and electron-lattice interaction. A variational solution of the Boltzmann equation which allows the inclusion of phonon drag effects is derived. An anisotropic scattering time solution is also presented. Both of these solutions are applied to calculation of the attenuation coefficient in pure metals and dilute alloys. </p> <p> The theory of the effects of electron-electron collisions on the ultrasonic attenuation in metals is also examined. </p> / Thesis / Doctor of Philosophy (PhD)

Lattice-Boltzmann method(LBM), a promising new particle-based simulation technique for complex and multiscale fluid flows, has seen tremendous adoption in recent years in computational fluid dynamics. Even with a state-of-the-art LBM solver such as Palabos, a user still has to manually write his program using the library-supplied primitives. We propose an automated code generator for a class of LBM computations with the objective to achieve high performance on modern architectures. Tiling is a very important loop transformation used to improve the performance of stencil computations by exploiting locality and parallelism. In the first part of the work, we explore diamond tiling, a new tiling technique to exploit the inherent ability of most stencils to allow tile-wise concurrent start. This enables perfect load-balance during execution and reduces the frequency of synchronization required. Few studies have looked at time tiling for LBM codes. We exploit a key similarity between stencils and LBM to enable polyhedral optimizations and in turn time tiling for LBM. Besides polyhedral transformations, we also describe a number of other complementary transformations and post processing necessary to obtain good parallel and SIMD performance on modern architectures. We also characterize the performance of LBM with the Roofline performance model. Experimental results for standard LBM simulations like Lid Driven Cavity, Flow Past Cylinder, and Poiseuille Flow show that our scheme consistently outperforms Palabos–on average by3 x while running on 16 cores of a n Intel Xeon Sandy bridge system. We also obtain a very significant improvement of 2.47 x over the native production compiler on the SPECLBM benchmark.