Implicit scheme for hyperbolic conservation laws using non-oscillatory reconstruction in space and time

Duraisamy, K. and Baeder, J. D. (2007) Implicit scheme for hyperbolic conservation laws using non-oscillatory reconstruction in space and time. SIAM Journal on Scientific Computing, 29(6), pp. 2607-2620. (doi: 10.1137/070683271)

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Publisher's URL: http://dx.doi.org/10.1137/070683271

Abstract

The efficiency of high order accurate schemes for the solution of unsteady hyperbolic conservation laws is adversely affected by time-step restrictions that arise from monotonicity requirements. When applied to the solution of problems involving discontinuities, these restrictions render conventional high order implicit time integration schemes impractical. In the present study, a new single step second order implicit scheme that uses nonoscillatory reconstruction in space and time is presented. Both the spatial and temporal limiters are dependent on the evolving solution, and this nonlinearity allows for a circumvention of total variation diminishing bounds. Numerical results on model scalar and vector hyperbolic equations suggest that the scheme holds promise in achieving accurate and unconditionally nonoscillatory solutions.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Duraisamy, Mr Karthikeyan
Authors: Duraisamy, K., and Baeder, J. D.
College/School:College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
Journal Name:SIAM Journal on Scientific Computing
Publisher:Society for Industrial and Applied Mathematics
ISSN:1064-8275
ISSN (Online):1095-7197
Published Online:31 October 2007

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