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On formulations of discontinuous galerkin and related methods for conservation laws
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Huynh, H. T. |
| Copyright Year | 2014 |
| Description | A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods. |
| File Size | 1552312 |
| Page Count | 36 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_20140009969 |
| Archival Resource Key | ark:/13960/t3jx3cf69 |
| Language | English |
| Publisher Date | 2014-06-01 |
| Access Restriction | Open |
| Subject Keyword | Fluid Mechanics And Thermodynamics Costs Stability Computational Fluid Dynamics Unstructured Grids Mathematics Derivation Fourier Analysis Spectral Methods Conservation Laws Navier-stokes Equation Numerical Analysis Flux Density Differential Equations Proving Galerkin Method Delta Function Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
