Type
Text
Type
Dissertation
Advisor
Glimm, James | Samulyak, Roman | Deng, Yuefan | McGraw, Robert.
Date
2015-12-01
Keywords
generalized finite differences, Lagrangian fluid mechanics, particle method | Applied mathematics
Department
Department of Applied Mathematics and Statistics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/77554
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
The goal of this thesis is the study of Lagrangian particle methods for complex multiscale hydrodynamic problems. This research has been motivated by difficulties arising in traditional mesh-based methods for the simulation of certain classes of highly non-uniform, complex free surface or multiphase problems. For such problems, Eulerian meshes enhanced with special algorithms for resolving interfaces such as volume-of-fluid, the level set method, arbitrary Lagrangian Eulerian methods, or the method of front tracking which is a hybrid method involving a moving Lagrangian mesh over a fixed Eulerian mesh, are often used. In addition, they require adaptive mesh refinement (AMR). All these methods require complex computationally intensive algorithms for the generation and dynamic adaptation of high quality meshes. As the method of Smoothed Particle Hydrodynamics (SPH) proposes an attractive alternative to the problems mentioned above, a parallel SPH code has been developed in the 1st phase of the research. The standard SPH algorithms have been enhanced with new implementation of physics models (cavitation, boundary conditions etc.) and applied to the simulation of mercury targets interacting with strong proton pulses in support of the DOE Muon Accelerator Project (MAP). Simulations of MAP experiments that studied splashes of mercury driven by external energy deposition have been performed and good agreement with experimental data has been obtained [2]. But in the course of our work, severe accuracy problems and limitations of SPH have been observed. They confirmed studies published in last years that SPH has zero- convergence order, and is not accurate for many classes of problems. Motivated by the need to resolve SPH failures while preserving its advantages, we have proposed a new Lagrangian particle method [1, 3] for solving Euler equations for compressible inviscid fluid or gas flows. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles. The main features of the method are (1) exact conservation of mass, (2) continuous adaptivity to density changes enabling simulations of large, non-uniform domains, (3) ability to handle material interfaces of any complexity, (4) scalability on modern supercomputers, (5) insignificant increase of algorithmic complexity with increase of spatial dimensionality leading to relatively simple codes in 3D. This also simplifies the portability of codes to new supercomputer architectures. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit and the corresponding weighted least squares problem and convergence of prescribed order, (b) an upwinding second-order particle- based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces using ghost particles. Numerical verification test demonstrating the convergence order are presented as well as examples of three- dimensional complex free surface flows. | 140 pages
Recommended Citation
Chen, Hsin-Chiang, "Convergent Lagrangian Particle Algorithms for Compressible Fluid Dynamics" (2015). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 3354.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/3354