TY - JOUR
T1 - Wave properties of fourth-order fully implicit Runge-Kutta time integration schemes
AU - Bhaumik, Swagata
AU - Sengupta, Soumyo
AU - Sengupta, Aditi
PY - 2013/7/20
Y1 - 2013/7/20
N2 - A global spectral analysis of fully implicit, two-stage, fourth-order Runge-Kutta method (IRK2) is presented here. The essential numerical properties of the IRK2 time-integration scheme, viz., nodal amplification factor, phase speed and group velocity have been quantified and plotted at all the nodal points of the computational domain as functions of the CFL (Courant-Friedrichs-Lewy number) and wavenumber for various explicit and implicit spatial discretization schemes. Results show that IRK2 scheme produces neutral stability at all interior nodes for all CFL numbers. This has been shown that while using IRK2 scheme one has to use refined grid at high CFL numbers for dispersion relation preservation property.
AB - A global spectral analysis of fully implicit, two-stage, fourth-order Runge-Kutta method (IRK2) is presented here. The essential numerical properties of the IRK2 time-integration scheme, viz., nodal amplification factor, phase speed and group velocity have been quantified and plotted at all the nodal points of the computational domain as functions of the CFL (Courant-Friedrichs-Lewy number) and wavenumber for various explicit and implicit spatial discretization schemes. Results show that IRK2 scheme produces neutral stability at all interior nodes for all CFL numbers. This has been shown that while using IRK2 scheme one has to use refined grid at high CFL numbers for dispersion relation preservation property.
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U2 - 10.1016/j.compfluid.2013.04.007
DO - 10.1016/j.compfluid.2013.04.007
M3 - Article
AN - SCOPUS:84878165094
SN - 0045-7930
VL - 81
SP - 110
EP - 121
JO - Computers and Fluids
JF - Computers and Fluids
ER -