Embedded entropy concept for fluid dynamic simulations with discontinuous Galerkin scheme
Abstract/Contents
- Abstract
- The Discontinuous Galerkin (DG) method represents an attractive simulation technique for computational fluid dynamics. Compared to conventional finite-difference and finite-volume methods, the DG method enables the high-order discretization on unstructured meshes, utilizes a compact discretization, and is well suited for advanced refinement strategies. However, it has been recognized that high-order DG approximations suffer robustness when applied to solving nonlinear conservation laws. These nonlinear numerical instabilities arise at physical discontinuities and numerically under-resolved flow-field features. By addressing these issues, this thesis work is concerned with the development of a realizable and stable high-order DG method for application to complex flows, involving discontinuities, shocks, and chemical reaction. An entropy-bounded discontinuous Galerkin (EBDG) scheme is developed, and the scheme is proven to preserve physical realizability of flow variables, such as the positivity of pressure and density, the boundedness of transported scalars and the boundedness of minimum entropy. In numerical tests, the EBDG scheme shows superb numerical stability and capability of capturing strong shock waves, as well as preservation of high-order accuracy for smooth solutions. The EBDG scheme is further augmented with a shock indicator and an artificial viscosity method to eliminate the Gibbs phenomenon triggered around shock discontinuities. The numerical framework developed based on the EBDG scheme is applied to study detonation initiation by shock-wall interaction. Specific focus of this study is on characterizing the role of Mach shock reflection on ignition and initiation processes. Furthermore, the accuracy and computational cost of the DG solver is assessed against a state-of-the-art finite volume solver in the applications to direct numerical simulations and large-eddy simulations of decaying turbulence. The comparison shows that on regular hexahedral meshes the finite volume scheme only requires one third of flops needed for the DG scheme at the same level of accuracy, while on tetrahedral meshes the DG scheme outperforms the finite volume scheme due to its capability of preserving the higher-order accuracy on unstructured and irregular meshes.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Lv, Yu |
|---|---|
| Associated with | Stanford University, Department of Mechanical Engineering. |
| Primary advisor | Ihme, Matthias |
| Thesis advisor | Ihme, Matthias |
| Thesis advisor | Lele, Sanjiva K. (Sanjiva Keshava), 1958- |
| Thesis advisor | Moin, Parviz |
| Advisor | Lele, Sanjiva K. (Sanjiva Keshava), 1958- |
| Advisor | Moin, Parviz |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Yu Lv. |
|---|---|
| Note | Submitted to the Department of Mechanical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Yu Lv
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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