A new incompressibility discretization for a hybrid particle MAC grid representation with surface tension
Abstract/Contents
- Abstract
- This dissertation takes a particle based approach to incompressible free surface flow motivated by the fact that an explicit representation of the interface geometry and internal deformations gives precise feedback to an implicit solver for surface tension. Methods that enforce incompressibility directly on the particles are typically numerically inefficient compared to those that utilize a background grid. However, background grid discretizations suffer from inaccuracy near the free surface where they do not properly capture the interface geometry. Therefore, this dissertation proposes a novel incompressibility discretization which utilizes a particle based projection near the interface and a background MAC grid based projection for efficiency in the vast interior of the liquid domain -- as well as a novel method for coupling these two disparate projections together. It is shown that the overall coupled elliptic solver is second order accurate, and remains second order accurate when used in conjunction with an appropriate temporal discretization for parabolic problems. A similar second order accurate discretization is derived when the MAC grid unknowns are located on faces (as opposed to cell centers) so that Navier-Stokes viscosity can be solved for implicitly as well. Finally, this dissertation presents a fully implicit approach to surface tension that is robust enough to achieve a steady state solution in a single time step. Beyond stable implicit surface tension for the novel hybrid discretization proposed in this dissertation, preliminary results are also demonstrated for both standard front tracking and the particle level set method.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Zheng, Wen |
|---|---|
| Associated with | Stanford University, Department of Computer Science. |
| Primary advisor | Fedkiw, Ronald P, 1968- |
| Thesis advisor | Fedkiw, Ronald P, 1968- |
| Thesis advisor | Levis, Philip |
| Thesis advisor | Savarese, Silvio |
| Advisor | Levis, Philip |
| Advisor | Savarese, Silvio |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Wen Zheng. |
|---|---|
| Note | Submitted to the Department of Computer Science. |
| Thesis | Ph.D. Stanford University 2013 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Wen Zheng
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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