| Author: | Yu, Lujia |
| Title: | Two-dimensional stabilized node-based smoothed particle finite element method for fluid flows and their interaction with structures in offshore engineering |
| Advisors: | Yin, Zhenyu (CEE) |
| Degree: | Ph.D. |
| Year: | 2024 |
| Subject: | Fluid-structure interaction -- Mathematical models Fluid dynamics Offshore structures Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Civil and Environmental Engineering |
| Pages: | xx, 242 pages : color illustrations |
| Language: | English |
| Abstract: | In offshore engineering, numerical simulations generally involve free-surface flows and structures. Each phase corresponds to distinct constitutive models, with interface and contact schemes in between. The particle finite element method (PFEM) stands out as an efficient numerical algorithm for offshore engineering. Based on the original PFEM, the node-based smoothed PFEM (NS-PFEM) addresses variable mapping challenges, reducing computational costs and interpolation errors. To further tackle temporal and spatial instabilities, the stabilized nodal integration is incorporated into NS-PFEM, resulting in the stabilized NS-PFEM (SNS-PFEM). Within the SNS-PFEM framework, various integration methods and coupling algorithms are compared to enhance fluid-structure-interaction (FSI) analysis performance. Additionally, different constitutive models for non-Newtonian fluid are explored to accurately describe granular/debris flow and multi-phase analysis in offshore engineering. In simulations using the NS-PFEM for incompressible flow, spatial and temporal instabilities have been identified as crucial issues. To address these challenges, this thesis introduces the SNS-PFEM formulation for simulating incompressible flows with free-surface: (1) Spatial integration stabilization is achieved by replacing the constant strain field with the gradient strain field over the smoothing domains, mitigating the instabilities in direct nodal integration; (2) Based on the finite increment calculus (FIC) technique, the stabilization terms for fluid computation are incorporated using nodal integration, and a three-step fraction step method (FSM) is adopted to update pressures and velocities; (3) A novel slip boundary with a predictor-corrector algorithm is developed to address interactions between free-surface flow and rigid walls, avoiding pressure concentration induced by the standard no-slip condition. The proposed SNS-PFEM-FIC is validated through several classical numerical cases. Comparisons with experimental results and other numerical solutions demonstrate its strong ability to accurately solve incompressible free-surface flow, with promising application prospects. In addition to pure fluids, FSI analysis should be carefully considered in offshore engineering. Although there has been some research on time integration and FSI coupling methods within the PFEM framework, their combined performance has not received specific attention. Consequently, this study introduces the SNS-PFEM formulation for FSI analysis involving incompressible free-surface flow: (1) The Newmark-β (NB) and Generalized-α (GA) time integration methods are implemented and compared using different parameters; (2) The Black-box Gauss-Seidel iteration with Atiken relaxation (BGS-Atiken) and the Interface Quasi-Newton Inverse Least Square (IQN-ILS) scheme are adopted and compared for FSI coupling; (3) Combined performance of the time integration and FSI coupling schemes is thoroughly investigated, offering simple guidance for parameter selection in complex FSI problems using SNS-PFEM. Comparisons are conducted across various 2D numerical cases, demonstrating the versatility and extensibility of the proposed algorithms. Subaerial and submarine landslides, which involve granular/debris flow and require multi-phase analysis, pose crucial challenges in offshore geotechnical engineering. However, the standard non-Newtonian fluid model, such as the Bingham model, is not sufficient to correctly describe the large motions associated with these problems. Additionally, the standard NS-PFEM can also introduce computational instability. Therefore, the SNS-PFEM formulation for granular/debris flow involving non-Newtonian fluid is presented in this thesis: (1) The standard elemental integration in PFEM using triangular T3 elements for incompressible non-Newtonian flow is replaced by stabilized nodal integration; (2) Various non-Newtonian models, including Bingham, Herschel-Bulkley, and μ(I) models, are adopted and regularized for specific cases with different materials; (3) Complicated multi-phase problems involving fluid mixing and structure reaction are simulated within the SNS-PFEM framework. The implementation and comparison are conducted through various numerical cases, demonstrating the good performance of the proposed algorithms for multi-phase analysis in offshore engineering. |
| Rights: | All rights reserved |
| Access: | open access |
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