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High-order hyperbolic residual-distribution schemes on arbitrary triangular grids
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Mazaheri, Alireza Nishikawa, Hiroaki |
| Copyright Year | 2015 |
| Description | In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation. |
| File Size | 5418221 |
| Page Count | 40 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_20160005986 |
| Archival Resource Key | ark:/13960/t5jb15f2t |
| Language | English |
| Publisher Date | 2015-06-22 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Linear Systems Boundary Value Problems Fourier Analysis Iteration Diffusivity Laser Anemometers Convergence Navier-stokes Equation Accuracy Advection Precision Linearity Skewness Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Article |
