TY - JOUR
T1 - On the Linear Stability of the Fifth-Order WENO Discretization
AU - Motamed, Mohammad
AU - Macdonald, Colin B.
AU - Ruuth, Steven J.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2010/10/3
Y1 - 2010/10/3
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/599059
UR - http://link.springer.com/10.1007/s10915-010-9423-9
UR - http://www.scopus.com/inward/record.url?scp=79959593384&partnerID=8YFLogxK
U2 - 10.1007/s10915-010-9423-9
DO - 10.1007/s10915-010-9423-9
M3 - Article
SN - 0885-7474
VL - 47
SP - 127
EP - 149
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 2
ER -