Robust and accurate shock-capturing in discontinuous Galerkin discretizations
Abstract/Contents
- Abstract
- Computational Fluid Dynamics (CFD) has become a critical component in analyzing fluid flows and designing industrial products. Among various numerical methods in CFD, second-order numerical schemes have been widely used in both industry and academia. Second-order methods are robust enough to use on complex geometries and usually provide a sufficient amount of accuracy in flow simulations. However, second-order accurate solutions may not be sufficient for many aerodynamic applications such as vortex flows, Large Eddy Simulations (LES), and aeroacoustics problems. As a consequence, researchers have sought high-order numerical methods to simulate complex flows with low dissipation over the past few decades. Many approaches have been suggested including Finite Difference (FD), Finite Volume (FV), and Finite Element (FE) frameworks for CFD. In the group of high-order methods, discontinuous Galerkin (DG) methods have become popular in academia because of their distinctive benefits. For DG methods, high-order accuracy in flow solutions can be easily achieved by just adding more degrees of freedom in each element. Furthermore, DG methods are well suited to modern computer hardware, even on GPUs, due to high arithmetic intensity and the locality of operations. Despite their numerous benefits, DG methods are not widely adopted because of some remaining challenges, especially in industry. One of these difficulties is shock-capturing. Similarly to other numerical methods in CFD, DG methods also suffer from spurious oscillations if discontinuities arise during flow simulations. The accuracy of solutions will degrade significantly, or solutions may diverge unless these discontinuities are captured appropriately. Therefore, a shock-capturing capability becomes necessary for DG methods to simulate compressible flows with shocks. In this work, robust and accurate shock-capturing approaches for DG methods will be demonstrated. To precisely capture various strengths of shocks, a simple shock-detector is first proposed for DG discretizations, which only relies on local flow information. Additionally, filtering strengths are precalculated to avoid parameter tuning procedures and are optimized to achieve maximum accuracy while capturing shocks. The proposed methods are then applied to two- and three-dimensional canonical problems to demonstrate the shock-capturing capabilities of the proposed methods.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2019; ©2019 |
| Publication date | 2019; 2019 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Choi, Jae Hwan |
|---|---|
| Degree supervisor | Alonso, Juan José, 1968- |
| Thesis advisor | Alonso, Juan José, 1968- |
| Thesis advisor | Cantwell, Brian |
| Thesis advisor | Lele, Sanjiva K. (Sanjiva Keshava), 1958- |
| Degree committee member | Cantwell, Brian |
| Degree committee member | Lele, Sanjiva K. (Sanjiva Keshava), 1958- |
| Associated with | Stanford University, Department of Aeronautics and Astronautics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Jae Hwan Choi. |
|---|---|
| Note | Submitted to the Department of Aeronautics and Astronautics. |
| Thesis | Thesis Ph.D. Stanford University 2019. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2019 by Jae Hwan Choi
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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