Date of Award

Winter 3-1-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Don Liu

Abstract

With the increase in computing power, numerical simulation has become an essential approach to solving problems in engineering and science. Numerical simulations provide a platform for theoretical validation and facilitate novel discovery. Even though extensive mesh-based numerical methods are utilized, significant limitations exist, particularly in Computational Fluid Dynamics (CFD). Because of the grid distortion, issues related to large deformations, moving interfaces, and free surfaces may lead to considerable computational errors, constraining their efficacy in numerous applications. As a mesh-free method, Smoothed Particle Hydrodynamics (SPH) was introduced in 1977 and has been widely applied in many fields such as astrophysics and hydrodynamics (D. a. Liu 2015). Free surface flow problems are covered in various domains, including hydraulic engineering, mechanical engineering, ship hydrodynamics, and petrochemical engineering. Hence, studying the free surface flow problem has theoretical and practical significance. Due to the advantages of SPH in handling large deformations and free boundaries, SPH is particularly suitable for free surface flow problems. Furthermore, new achievements in computational power improve computing efficiency; this enables SPH to simulate complex free surface flows. This dissertation studies the validation of SPH for free surface flow applications and explores a time series forecasting method to enhance CFD. There are four main contributions to this dissertation: First, we introduce artificial viscosity into SPH. In the meantime, this improved method is shown through demos of free surface flow in different cases. Second, based on the demos of the improved SPH method in Chapter 3, we discuss the water break models to explore the further application of SPH in complex coastal environments in Chapter 4. We also analyze the interaction between waves and various water break designs. Then, we assess the effects of different structures on wave overtopping to identify the optimal water break configuration. Third, we address the importance of water level research by examining water break models. In Chapter 5, with historical water level data from the Mississippi River, we discuss a time series analysis model based on ARIMA to forecast future water levels. The forecast results are in line with the actual trend. Finally, we show how GPU parallel computation dramatically improves the simulation efficiency of our model.

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