High Performance Free Surface LBM on GPUs

The lattice Boltzmann method (LBM) is a well established tool for simulating fluids, with its ability to model arbitrary geometries and function across a wide range of simulation parameters. By combining the LBM with the Volume-of-Fluid (VoF) model, free surfaces can be simulated. The algorithmic structure of LBM allows for hardware-near implementation on graphics processing units (GPUs), using their full capabilities. In this work, LBM is implemented from the ground up in OpenCL, a programming language specifically designed for massively parallel hardware, and this implementation is called FluidX3D. A large catalog of GPU-specific optimizations is incorporated in order to reach maximum efficiency, allowing for close to real-time simulations of complex free surface phenomena such as drop impacts with all the variety of emerging effects including crown- and jet-formation and the Plateau-Rayleigh instability. In the process of writing the simulation software, various flavors of the LBM in the form of velocity sets and collision operators are investigated and characterized. The most common extensions to the LBM are incorporated into the implementation, among them various boundary conditions volume forces, evaluation of boundary forces, a temperature model for simulating thermal convection, the immersed-boundary method for simulating fluid-particle interaction, the Shan-Chen model for simulating the coexistence of liquid and vapor and lastly the main focus of this work, the Volume-of-Fluid (VoF) model for simulating free surfaces with a sharp interface. The main difficulty of the latter, besides the challenge of running it alongside LBM with massive parallelism on the GPU, is surface curvature calculation, which has a geometry problem at its core, the plane-cube intersection as part of piecewise linear interface construction (PLIC), to which the complete analytic solution is elaborated and presented here. The base functionality of LBM is thoroughly validated with two setups where the analytic solution is known, Poiseuille flow in a cylindrical channel and laminar flow around a sphere. For validating the VoF model, mass conservation is checked and the accuracy of different approaches for curvature calculation is characterized. Then the model is verified qualitatively and quantitatively on a system with analytically known stability behavior: the Plateau-Rayleigh instability on an undulated cylinder of fluid. After validation of the implementation, the following systems are studied in detail: With the base LBM implementation, a simulation is done to find the force acting on a microplastic particle attached to the wall of a rectangular microchannel. The VoF model is used to recreate oblique drop impact and crown splashing setups and the simulation results are compared to experimental observations. Lastly, some qualitative simulations are shown in order to demonstrate the vast diversity of use-cases of the here developed LBM implementation and in order to show a few of the fascinating emerging effects in hydrodynamics.