High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids
Abstract
In this paper, we construct high-order hyperbolic residual-distribution schemes for gen- eral 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 the third-order by further requiring the exact- ness for cubic solutions. We construct these schemes based on the Low-Diffusion-A and the Streamwise-Upwind-Petrov-Galerkin methodology formulated in the framework of the residual-distribution method. For both second- and third-orderschemes, 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 also demonstrate that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the con- struction 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 per- formed on the constructed linear system and show that an underrelaxation parameter is needed for stabilization of Gauss-Seidel relaxation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 22, 2015
- Accession Number
- ADA624802
Entities
People
- Alireza Mazaheri
- Hiroaki Nishikawa
Organizations
- National Institute of Aerospace