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Progress in multi-dimensional upwind differencing
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Vanleer, Bram |
| Copyright Year | 1992 |
| Description | Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes. |
| File Size | 1574347 |
| Page Count | 32 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19930001620 |
| Archival Resource Key | ark:/13960/t0tr0tj3c |
| Language | English |
| Publisher Date | 1992-09-01 |
| Access Restriction | Open |
| Subject Keyword | Fluid Mechanics And Heat Transfer Shock Waves Wave Propagation Difference Equations Computational Fluid Dynamics S Waves Finite Difference Theory Euler Equations of Motion Finite Volume Method Mathematical Models Convection Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Article |
