A conservative meshless framework for conservation laws with applications in computational fluid dynamics
Abstract/Contents
- Abstract
- Mesh generation, which is essential to most traditional numerical discretizations, often remains the bottleneck of the simulation process. Many researchers have developed meshless algorithms to circumvent mesh generation. Unfortunately, almost all existing meshless methods suffer from the lack of formal discrete conservation, which can lead to unpredictable numerical errors in the presence of discontinuities. This thesis addresses the issue of non-conservation in existing meshless methods. It focuses on the formulation and implementation of a novel conservative meshless scheme and its applications in computational fluid dynamics (CFD). The scheme, first of such nature documented in the literature, is formulated based on obtaining derivative approximations using function values and generated coefficients satisfying a set of reciprocity and polynomial consistency conditions. The required coefficients are generated by the solution of a global quadratic program. They minimize an upper bound of a representation of the global discretization error in addition to satisfying the necessary conditions. A generalization of the derivative approximation allows the use of arbitrary consistent interface values in the derivative operator while maintaining discrete conservation. This creates a flexible framework within which a wide variety of numerical flux schemes, such as those previously developed for finite volume discretization, can be used with no additional costs. The practicality of this new framework is demonstrated by solving compressible flow problems using, without modifications, a piece of software designed for finite volume discretization. The meshless numerical results show superconvergence and compare well with those obtained using meshed finite volume discretizations and other meshless schemes, highlighting the validity of the new framework and its potential to be applied to problems of greater complexity and scale.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2011 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Chiu, Kwan Yu |
|---|---|
| Associated with | Stanford University, Department of Aeronautics and Astronautics |
| Primary advisor | Jameson, Antony, 1934- |
| Thesis advisor | Jameson, Antony, 1934- |
| Thesis advisor | Iaccarino, Gianluca |
| Thesis advisor | MacCormack, R. W. (Robert William), 1940- |
| Advisor | Iaccarino, Gianluca |
| Advisor | MacCormack, R. W. (Robert William), 1940- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Kwan Yu Chiu. |
|---|---|
| Note | Submitted to the Department of Aeronautics and Astronautics. |
| Thesis | Ph.D. Stanford University 2011 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2011 by Kwan Yu Chiu
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