On the development of the direct flux reconstruction scheme for high-order fluid flow simulations
Abstract/Contents
- Abstract
- In the past few years, there have been several emerging challenges facing the advancement of computational fluid dynamics (CFD) for aerospace design applications. Firstly, there is an growing interest in simulating unsteady, vortex-dominated flows over complex geometries, a problem for which existing second-order Reynolds-averaged Navier-Stokes (RANS) methods have had limited success. In addition to this, shifts in modern computing hardware towards highly data-parallel architectures, such as graphics processing units (GPU) and similar accelerators, have created another hurdle, as many existing CFD applications and methods are not well suited to draw compute performance efficiently from these increasingly dominant computing technologies. To address these challenges, there has been an increased interest in high-order CFD methods, in particular those based within a discontinuous finite element (DFE) framework. The high-order nature of these methods makes them well-suited to simulating vortex-dominated flows due to a limited introduction of numerical dissipation. Furthermore, the element-wise discretizations found within DFE methods result in tightly-coupled degrees of freedom within each element, a trait that maps well to modern computing hardware due to an increased potential for data reuse and high arithmetic intensity. A popular DFE method that is particularly suitable for solving the compressible Navier-Stokes equations is the flux reconstruction (FR) method. The FR method is based on the differential form of the governing equations and provides a general framework that can recover other similar high-order schemes, such as the nodal discontinuous Galerkin (DG) scheme and the spectral difference (SD) scheme. While existing FR methods are commonly touted as simple relative to comparable DFE methods, they still remain fairly complex relative to existing lower order alternatives. In this thesis, a simplified variation of the flux reconstruction scheme, named the direct flux reconstruction (DFR) scheme is developed which streamlines the existing flux reconstruction procedure, on tensor-product and simplex elements. The first part of the thesis contains the development of the DFR scheme in 1D and its extension to tensor-product elements for advection-diffusion type problems. The DFR formulation in this context is proven to be linearly stable and shown to recover the nodal DG method for 1D and tensor product elements. In latter chapters, an extension of the DFR scheme to simplex elements is developed beyond this which provides a new approach for FR on simplices that naturally extends many of the ideas from the 1D scheme. In addition to theoretical developments, this thesis includes details of a GPU implementation of the DFR scheme that achieves high-performance on modern computing hardware.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Romero, Joshua D |
|---|---|
| Associated with | Stanford University, Department of Aeronautics and Astronautics. |
| Primary advisor | Jameson, Antony, 1934- |
| Thesis advisor | Jameson, Antony, 1934- |
| Thesis advisor | Alonso, Juan José, 1968- |
| Thesis advisor | Farhat, Charbel |
| Advisor | Alonso, Juan José, 1968- |
| Advisor | Farhat, Charbel |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Joshua D. Romero. |
|---|---|
| Note | Submitted to the Department of Aeronautics and Astronautics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Joshua Daniel Romero
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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