A HYBRID LATTICE BOLTZMANN METHOD-POTENTIAL FLOW MODEL FOR NAVAL HYDRODYNAMICS

The simulation of many naval hydrodynamics problems, such as a ship’s motions in waves, is often performed using potential flow solvers which are usually based on a Boundary Element Method (BEM) that use semi-empirical corrections to account for viscous/turbulent effects. However in some cases, viscous/turbulent flows near the ships hull and breaking waves must be accurately modeled to capture the salient physics. Navier-Stokes (NS) solvers can and have been used to model such flows, but they are computationally expensive, often requiring several orders of magnitude more computational resources relative to potential flow methods, rendering them impracticable for many engineering applications. The overall goal of this work is to develop a naval hydrodynamics solver that leverages a medium-fidelity potential flow solver to model the entire domain combined with a high-fidelity Navier-Stokes (NS) solver to model the flow within a smaller region, where better accuracy is required. This hybrid solver provides improved simulation fidelity relative to a potential flow solution alone while a significant computational efficiency improvement relative to a NS solver alone is gained. Within the NS domain both the velocity and pressure are expressed as the sum of an inviscid (I) and viscous perturbation (P) components. The underlying inviscid solution serves to drive the perturbation component, which in turn provides a correction so that the total solution reproduces the NS equations. Considering that most naval hydrodynamics flows occur at high Renyolds numbers, the viscous region of the flow is often small, and can be applied to a reduced domain around a hull or to localized regions within the flow. Outside of these regions the salient viscous effects will become small and the inviscid solver provides the full NS solution. In this work the NS domain is simulated using the particle based Lattice Boltzmann Method (LBM). This relatively new computational tool has proved to be accurate and efficient for simulating a variety of complex fluid flow and fluid-structure interaction problems. It shows the potential for a competitive advantage over traditional finite volume NS solvers when implemented in parallel on Graphics Processing Units (GPUs). The LBM is well suited for the GPU architecture because its kernel is simple and local, so at each time step relatively small number of operations is required at each node and nodes only communicate with their neighbors. This is opposed to finite volume solvers which typically require high order derivatives and a global pressure correction step, where all nodes need to communicate and more complex memory access is required. Using the LBM our hybrid method can make efficient use of a computer’s resources by simulating the BEM using the central processing unit (CPU) nodes and simulating the LBM using a relatively inexpensive GPU addition, allowing for simulations that would otherwise require a large and expensive CPU cluster. The goal of this thesis is to develop a LBM that can solve for the perturbation component of our hybrid method, which requires a modification to the LBMs governing equations, boundary, and initial conditions. The first chapter describes the fundamental developments towards this goal of developing what we refer to as a perturbation LBM (pLBM) and presents several low Reynolds number validations of the method’s accuracy and convergence. The second chapter focuses on higher Reynolds number applications of the method. Since the LBM is far less established than other methods, this required that we develop an accurate turbulent wall boundary condition for standard LBM, which is currently an active area of research in the LBM community. Next the turbulent wall model and a large eddy simulation (LES) turbulent closure schemes are expressed for the pLBM by using the standard LBM methodology as a foundation and a validated for turbulent applications is presented. The third chapter focuses on the hybrid modeling of the nonlinear free surface and adapting the pLBM tool to simulate ship geometries. A hybrid volume of fluid (hVOF) free surface capturing scheme is developed which models the total free surface using a combination of the inviscid and perturbation flow within the pLBM. Finally, pLBM is coupled to a BEM solver to simulate the steady flow around a ship and the hVOF is used to simulate nonlinear and breaking waves.