Back to Search
Start Over
First-, second-, and third-order finite-volume schemes for diffusion.
- Source :
-
Journal of Computational Physics . Jan2014, Vol. 256, p791-805. 15p. - Publication Year :
- 2014
-
Abstract
- Abstract: In this paper, we present constructions of first-, second-, and third-order schemes for diffusion by the method introduced in Nishikawa (2007) [10]. In this method, numerical schemes for diffusion are constructed by advection schemes via an equivalent hyperbolic system. This paper demonstrates that the method enables straightforward constructions of diffusion schemes for finite-volume methods on unstructured grids. In particular, it is demonstrated that a robust first-order upwind scheme leads to a robust first-order diffusion scheme, and a high-order advection scheme leads to a high-order diffusion scheme. It is shown that first-, second-, and third-order schemes are capable of producing first-, second-, and third-order accurate solution gradients, respectively, on irregular grids. Accuracy, Fourier stability, and the energy stability of the developed schemes are discussed. A new hyperbolic diffusion system having virtually no source terms is also introduced to simplify the construction of the third-order scheme. Numerical results are presented for regular and irregular triangular grids to demonstrate not only the superior accuracy but also the accelerated steady convergence over a traditional method. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 256
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 91573843
- Full Text :
- https://doi.org/10.1016/j.jcp.2013.09.024