Energy stable high-order methods for simulating unsteady, viscous, compressible flows on unstructured grids
Abstract/Contents
- Abstract
- High-order methods have the potential to dramatically improve the accuracy and efficiency of flow simulations in the field of computational fluid dynamics (CFD). However, there remain questions regarding the stability and robustness of high-order methods for practical problems on unstructured triangular and tetrahedral grids. In this work, a new class of 'energy stable' high-order methods is identified. This class of schemes (referred to as the 'Energy Stable Flux Reconstruction' class of schemes) is proven to be stable for linear advection-diffusion problems, for all orders of accuracy on unstructured triangular grids in 2D and unstructured tetrahedral grids in 3D. Furthermore, this class of schemes is shown to be capable of recovering the well-known collocation-based nodal discontinuous Galerkin scheme, along with new schemes that possess explicit time-step limits which are (in some cases) more than 2x larger than those of the discontinuous Galerkin scheme. In addition, the stability of the Energy Stable Flux Reconstruction schemes is examined for nonlinear problems, and it is shown that stability depends on the degree of nonlinearity in the flux and on the placement of solution and flux points in each element. In particular, it is shown that choosing the solution and flux point locations to coincide with the locations of quadrature points promotes nonlinear stability by minimizing (or eliminating) nonlinear aliasing errors. A new class of symmetric quadrature points is identified on triangles and tetrahedra for this purpose. Finally, the Energy Stable Flux Reconstruction schemes and the new quadrature points are applied to several nonlinear problems with the aim of assessing how well the schemes perform in practice.
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 | Williams, David Michael |
|---|---|
| Associated with | Stanford University, Department of Aeronautics and Astronautics. |
| Primary advisor | Jameson, Antony, 1934- |
| Thesis advisor | Jameson, Antony, 1934- |
| Thesis advisor | Farhat, Charbel |
| Thesis advisor | MacCormack, R. W. (Robert William), 1940- |
| Advisor | Farhat, Charbel |
| Advisor | MacCormack, R. W. (Robert William), 1940- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | David Michael Williams. |
|---|---|
| Note | Submitted to the Department of Aeronautics and Astronautics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by David Michael Williams
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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