lattice boltzmann

"Lattice Boltzmann methods (LBM) (or thermal Lattice Boltzmann methods (TLBM)) is a class of computational fluid dynamics (CFD) methods for fluid simulation. Instead of solving the Navier–Stokes equations, the discrete Boltzmann equation is solved to simulate the flow of a Newtonian fluid with collision models such as Bhatnagar–Gross–Krook (BGK). By simulating streaming and collision processes across a limited number of particles, the intrinsic particle interactions evince a microcosm of viscous flow behavior applicable across the greater mass.

LBM is a relatively new simulation technique for complex fluid systems and has attracted interest from researchers in computational physics. Unlike the
traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh. Due to its particulate nature and local dynamics, LBM has several advantages over other conventional CFD methods, especially in dealing with complex boundaries, incorporating microscopic interactions, and parallelization of the algorithm. A different interpretation of the Lattice Boltzmann equation is that of a discrete-velocity Boltzmann equation. The numerical methods of solution of the system of partial differential equations then gives rise to a discrete map, which can be interpreted as the propagation and collision of fictitious particles.

The advantages are:

• The LBM method was designed from scratch to run efficiently on massively parallel architectures, ranging from inexpensive embedded FPGAs and DSPs up to GPUs and heterogeneous clusters and supercomputers (even with a slow interconnection network). It enables complex physics and sophisticated algorithms. Efficiency leads to a qualitatively new level of understanding, since it allows solving problems that previously could not be approached (or only with insufficient accuracy).
• The method originates from a molecular description of a fluid and can directly incorporate physical terms stemming from a knowledge of the interaction between molecules. Hence it is an indispensable instrument in fundamental research, as it keeps the cycle between the elaboration of a theory and the formulation of a corresponding numerical model short.
• Automated data pre-processing and mesh generation in a time that accounts for a small fraction of the total simulation.
• Parallel data analysis, post-processing and evaluation.
• Fully resolved multi-phase flow with small droplets and bubbles.
• Fully resolved flow through complex geometries and porous media.
• Complex, coupled flow with heat transfer and chemical reactions.

Despite the increasing popularity of LBM in simulating complex fluid systems, this novel approach has some limitations. At present, high-Mach number flows in aerodynamics are still difficult for LBM, and a consistent thermo-hydrodynamic scheme is absent. However, as with Navier–Stokes based CFD, LBM methods have been successfully coupled to thermal-specific solutions to enable heat transfer (solids-based conduction, convection and radiation) simulation capability. For multiphase/multicomponent models, the interface thickness is usually large and the density ratio across the interface is small when compared with real fluids. Recently this problem has been resolved by Yuan and Schaefer who improved on models by Shan and Chen, Swift, and He, Chen, and Zhang. They were able to reach density ratios of 1000:1 by simply changing the equation of state."

https://en.wikipedia.org/wiki/Lattice_Boltzmann_methods

Performance and Portability of Accelerated Lattice Boltzmann Applications with OpenACC - http://hgpu.org/?p=17029

Optimization of Lattice Boltzmann Simulations on Heterogeneous Computers - https://arxiv.org/abs/1703.04594

Lattice Boltzmann modeling of water-like fluids - http://journal.frontiersin.org/article/10.3389/fphy.2014.00022/full