A Meshfree-Based Lattice Boltzmann Approach for Simulation of Fluid Flows Within Complex Geometries

This chapter develops a meshless formulation of lattice Boltzmann method for simulation of fluid flows within complex and irregular geometries. The meshless feature of proposed technique will improve the accuracy of standard lattice Boltzmann method within complicated fluid domains. Discretization of such domains itself may introduce significant numerical errors into the solution. Specifically, in phase transition or moving boundary problems, discretization of the domain is a time-consuming and complex process. In these problems, at each time step, the computational domain may change its shape and need to be re-meshed accordingly for the purpose of accuracy and stability of the solution. The author proposes to combine lattice Boltzmann method with a Galerkin meshfree technique popularly known as element-free Galerkin method in this chapter to remove the difficulties associated with traditional grid-based methods.

Large Eddy Simulation Turbulence Model Applied to the Lattice Boltzmann Method

The lattice Boltzmann method (LBM) is a novel approach for simulating convection-diffusion problems. It can be easily parallelized and hence can be used to simulate fluid flow in multi-core computers using parallel computing. LES (large eddy simulation) is widely used in simulating turbulent flows because of its lower computational needs compared to others such as direct numerical simulation (DNS), where the Kolmogorov scales need to be solved. The aim of this chapter consists of introducing the reader to the treatment of turbulence in fluid dynamics through an LES approach applied to LBM. This allows increasing the robustness of LBM with lower computational costs without increasing the mesh density in a prohibitive way. It is applied to a standard D2Q9 structure using a unified formulation.

Fluid-Structure Interaction Using Lattice Boltzmann Method Coupled With Finite Element Method

This chapter presents several partitioned algorithms to couple lattice Boltzmann method (LBM) and finite element method (FEM) for numerical simulation of transient fluid-structure interaction (FSI) problems with large interface motion. Partitioned coupling strategies allow one to solve separately the fluid and solid subdomains using adapted or optimized numerical schemes, which provides a considerable flexibility for FSI simulation, especially for more realistic and industrial applications. However, partitioned coupling procedures often encounter numerical instabilities due to the fact that the time integrations of the two subdomains are usually carried out in a staggered way. As a consequence, the energy transfer across the fluid-solid interface is usually not correctly simulated, which means numerical energy injection or dissipation might occur at the interface with partitioned methods. The focus of the present chapter is given to the energy conservation property of different partitioned coupling strategies for FSI simulation.

Wake Interaction Using Lattice Boltzmann Method

In this chapter, a brief discussion about the application of lattice Boltzmann method on complex flow characteristics over circular structures is presented. A two-dimensional computational simulation is performed to study the fluid flow characteristics by employing the lattice Boltzmann method (LBM) with respect to Bhatnagar-Gross-Krook (BGK) collision model to simulate the interaction of fluid flow over the circular cylinders at different spacing conditions. From the results, it is observed that there is no significant interaction between the wakes for the transverse spacing's ratio higher than six times the cylinder diameter. For smaller transverse spacing ratios, the fluid flow regimes were recognized with presence of vortices. Apart from that, the drag coefficient signals are revealed as chaotic, quasi-periodic, and synchronized regimes, which were observed from the results of vortex shedding frequencies and fluid structure interaction frequencies. The strength of the latter frequency depends on spacing between the cylinders; in addition, the frequency observed from the fluid structure interaction is also associated with respect to the change in narrow and wide wakes behind the surface of the cylinder. Further, the St and mean Cd are observed to be increasing with respect to decrease in the transverse spacing ratio.

Challenges on Porting Lattice Boltzmann Method on Accelerators

Currently NVIDIA GPUs and Intel Xeon Phi accelerators are alternatives of computational architectures to provide high performance. This chapter investigates the performance impact of these architectures on the lattice Boltzmann method. This method is an alternative to simulate fluid flows iteratively using discrete representations. It can be adopted for a large number of flows simulations using simple operation rules. In the experiments, it was considered a three-dimensional version of the method, with 19 discrete directions of propagation (D3Q19). Performance evaluation compare three modern GPUs: K20M, K80, and Titan X; and two architectures of Xeon Phi: Knights Corner (KNC) and Knights Landing (KNL). Titan X provides the fastest execution time of all hardware considered. The results show that GPUs offer better processing time for the application. A KNL cache implementation presents the best results for Xeon Phi architectures and the new Xeon Phi (KNL) is two times faster than the previous model (KNC).

Design and Optimizations of Lattice Boltzmann Methods for Massively Parallel GPU-Based Clusters

GPUs deliver higher performance than traditional processors, offering remarkable energy efficiency, and are quickly becoming very popular processors for HPC applications. Still, writing efficient and scalable programs for GPUs is not an easy task as codes must adapt to increasingly parallel architecture features. In this chapter, the authors describe in full detail design and implementation strategies for lattice Boltzmann (LB) codes able to meet these goals. Most of the discussion uses a state-of-the art thermal lattice Boltzmann method in 2D, but all lessons learned in this particular case can be immediately extended to most LB and other scientific applications. The authors describe the structure of the code, discussing in detail several key design choices that were guided by theoretical models of performance and experimental benchmarks, having in mind both single-GPU codes and massively parallel implementations on commodity clusters of GPUs. The authors then present and analyze performances on several recent GPU architectures, including data on energy optimization.

Lattice Boltzmann Method for Sparse Geometries

This chapter presents the challenges and techniques in the efficient LBM implementations for sparse geometries. The first part contains a review of applications requiring support for sparse geometries including industry, geology, and life sciences. For each category, a short description of a geometry characteristic and the typical LBM extensions are provided. The second part describes implementations for single-core and parallel computers. Four main methods allowing for the reduction of memory usage and computational complexity are presented: hierarchical grids, tiles, and two techniques based on the indirect addressing (the fluid index array and the connectivity matrix). For parallel implementations, the advantages and disadvantages of the different methods of domain decomposition and workload balancing are discussed.

Lattice Boltzmann Shallow Water Simulation With Surface Pressure

Shallow water conditions are produced in coastal and river areas and allow the simplification of fluid solving by integrating in height to the fluid equations, discarding vertical flow so a 3D problem is solved with a set of 2D equations. Usually the boundary conditions defined by the surface pressure are discarded, as it is considered that the difference in atmospheric pressure in simulation domain is irrelevant in most hydraulic and coastal engineering scenarios. However, anticyclones and depressions produce noticeable pressure gradients that may affect the consequences of phenomena like tides and tsunamis. This chapter demonstrates how to remove this weakness from the LBM-SW by incorporating pressure into the LBM for this kind of scenario in a consistent manner. Other small-scale effects like buoyancy may be solved using this approach.

Mesh Refinement for LBM Simulations on Cartesian Meshes

The use of mesh refinement in CFD is an efficient and widely used methodology to minimize the computational cost by solving those regions of high geometrical complexity with a finer grid. The author focuses on studying two methods, one based on multi-domain and one based on irregular meshing, to deal with mesh refinement over LBM simulations. The numerical formulation is presented in detail. Two approaches, homogeneous GPU and heterogeneous CPU+GPU, on each of the refinement methods are studied. Obviously, the use of the two architectures, CPU and GPU, to compute the same problem involves more important challenges with respect to the homogeneous counterpart. These strategies are described in detail paying particular attention to the differences among both methodologies in terms of programmability, memory management, and performance.

Programming and Computing Lattice Boltzmann Method

The use of lattice Boltzmann method (LBM) has been extended to numerous fields of scientific and industrial interest due to its inherent characteristics, which make this methodology a very efficient and fast method for fluid simulations. In this chapter, the numerical formulation behind LBM is presented in detail. However, the main motivation of this chapter is the introduction to those aspects regarding the programmability of this method. The authors present different implementations, data layout, and strategies to efficiently implement LBM. The performance achieved by each of the techniques is analyzed in detail, over some of the currently used computer platforms. They pay particular attention to those techniques that attempt to reduce the memory requirement of their method, which is one of the most important weak-points when implementing and computing LBM.