

Author: Karni S. Kurganov A. Petrova G.
Publisher: Academic Press
ISSN: 0021-9991
Source: Journal of Computational Physics, Vol.178, Iss.2, 2002-05, pp. : 323-341
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
The formation of shock waves in solutions of hyperbolic conservation laws calls for locally adaptive numerical solution algorithms and requires a practical tool for identifying where adaption is needed. In this paper, a new smoothness indicator (SI) is used to identify “rough” solution regions and is implemented in locally adaptive algorithms. The SI is based on the weak local truncation error of the approximate solution. It was recently reported in S. Karni and A. Kurganov, Local error analysis for approximate solutions of hyperbolic conservation laws, where error analysis and convergence properties were established. The present paper is concerned with its implementation in scheme adaption and mesh adaption algorithms. The SI provides a general framework for adaption and is not restricted to a particular discretization scheme. The implementation in this paper uses the central-upwind scheme of A. Kurganov, S. Noelle, and G. Petrova,
Related content


Wave Propagation Algorithms for Multidimensional Hyperbolic Systems
By LeVeque R.J.
Journal of Computational Physics, Vol. 131, Iss. 2, 1997-03 ,pp. :




Absolutely representing systems, uniform smoothness and type
By Vershynin R.
Quaestiones Mathematicae, Vol. 23, Iss. 1, 2000-03 ,pp. :




Upwind scheme for non-hyperbolic systems
By Hwang Y.-H.
Journal of Computational Physics, Vol. 192, Iss. 2, 2003-12 ,pp. :