A single-step and GPU-accelerated simplified lattice Boltzmann method for high turbulent flows on complex domains

Abstract

Over the course of time, Computational Fluid Dynamics (CFD) has been proven to be one of the main pillars in the study of fluid mechanics. From simple aerodynamic designs to highly complex meteorological forecast, CFD models have been served as one of the best tools used for designers and engineers. Nevertheless, high fidelity CFD simulations often require a considerable amount of computational power in order to deliver accurate results. For this, the exponential growth of computational technologies has been helping to solve this problem, but significant computational cost can be reduced by improving the main theory for the numerical simulation. The Lattice Boltzmann Method (LBM) is a relatively new approach for the simulation of fluid dynamics. It has been proven that the overall computational efficiency of the LBM is critically better than the conventional Direct Numerical Simulations for the Navier-Stokes Equations. However, the conventional LBM algorithms are considerably limited for very specific simulation cases, such as fluid flows in a small range of the Reynolds number. This dissertation presents in detail a novel CFD model derived by combining the theory of conventional and more recent algorithms for the Single-relaxation time (SRT) LBM. The present model is entitled "Single-Step and Simplified Lattice Boltzmann Method" (SS-LBM) and is capable of delivering efficient and accurate results of fluid dynamics in a wide range of the Reynolds number, by coupling the main algorithm with an efficient sub-grid scale (SGS) turbulence model. Additionally, the SS-LBM model is also designed to simulate complex terrains, by generating the domain mesh with a parametric geometry based on the bi-variate (2D) and tri-variate (3D) Non-Uniform Rational B-Splines (NURBS) functions.In order to significantly improve the computational performance of the SS-LBM model, the main algorithm is designed for the execution on Graphics Processing Unit (GPU) architectures, through the well known OpenGL framework. By retaining the best properties of the recent LBM algorithms such as the Simplified-LBM (SLBM), the present model minimizes the memory size needed by only allocating the macroscopic flow variables (velocity and density), which are the main variables used to reconstruct the required probability distribution functions (pdf). The complete algorithm is tested by conducting numerous benchmark cases to validate and quantify the computational performance and spatial accuracy. For the 2D cases, the 2D Lid-Driven Cavity (LDC) benchmark for a wide range of the Reynolds number is reported, along with the simulation of the fluid flow across a 2D circle and NACA airfoils. For the 3D cases, a 3D LDC benchmark is also performed, followed by a 3D Jet-flow inside a cavity. Finally, the algorithm is tested for a case with a complex terrain with a local refinement around the desired surface.