Type
ArticleKAUST Grant Number
KUK-C1-013-04Date
2010-10-03Online Publication Date
2010-10-03Print Publication Date
2011-05Permanent link to this record
http://hdl.handle.net/10754/599059
Metadata
Show full item recordAbstract
We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.Citation
Motamed M, Macdonald CB, Ruuth SJ (2010) On the Linear Stability of the Fifth-Order WENO Discretization. Journal of Scientific Computing 47: 127–149. Available: http://dx.doi.org/10.1007/s10915-010-9423-9.Sponsors
The work of M. Motamed was partially supported by NSERC Canada.The work of C. B. Macdonald was supported by NSERC Canada, NSF grant number CCF-0321917, and by Award No KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).The work of S.J. Ruuth was partially supported by NSERC Canada.Publisher
Springer NatureJournal
Journal of Scientific Computingae974a485f413a2113503eed53cd6c53
10.1007/s10915-010-9423-9