scholarly journals Influence of order enhancement of the Runge-Kutta method on low-order turbulence statistics of incompressible wall turbulence under a second-order central difference scheme

2020 ◽  
Vol 1592 ◽  
pp. 012095
Author(s):  
Shotaro Jomura ◽  
Hiroki Suzuki ◽  
Yutaka Hasegawa ◽  
Shinnosuke Matsuo ◽  
Shinsuke Mochizuki
Keyword(s):  
Difference Scheme ◽  
Second Order ◽  
Wall Turbulence ◽  
Kutta Method ◽  
Turbulence Statistics ◽  
Central Difference ◽  
Central Difference Scheme ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Low Order

Symmetric and symplectic methods for gyrocenter dynamics in time-independent magnetic fields

2016 ◽  
Vol 07 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Beibei Zhu ◽  
Zhenxuan Hu ◽  
Yifa Tang ◽  
Ruili Zhang
Keyword(s):  
Numerical Simulation ◽  
Hamiltonian System ◽  
Second Order ◽  
Symplectic Methods ◽  
Kutta Method ◽  
Numerical Accuracy ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Runge Kutta

We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system. The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation. Furthermore, they are much faster than the midpoint rule applied to the canonicalized system to reach given precision.

An efficient implicit Runge–Kutta method for second order systems

2006 ◽  
Vol 178 (2) ◽  
pp. 229-238 ◽  
Author(s):  
Basem S. Attili ◽  
Khalid Furati ◽  
Muhammed I. Syam
Keyword(s):  
Second Order ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Second Order Systems
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