Parallel-iterated pseudo two-step Runge–Kutta methods with step size control

2014 ◽  
Vol 31 (2) ◽  
pp. 441-460
Author(s):  
Nguyen Huu Cong ◽  
Nguyen Thu Thuy
Keyword(s):  
Size Control ◽  
Step Size ◽  
Step Size Control ◽  
Runge Kutta

scholarly journals Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

2021 ◽  
Author(s):  
Hendrik Ranocha ◽  
Lisandro Dalcin ◽  
Matteo Parsani ◽  
David I. Ketcheson
Keyword(s):  
Fluid Dynamics ◽  
Error Control ◽  
Time Integration ◽  
Size Control ◽  
Spectral Element ◽  
Step Size ◽  
Step Size Control ◽  
Wide Range ◽  
Cfd Applications ◽  
Runge Kutta

AbstractWe develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice. We compare a wide range of error-control-based methods, along with the common approach in which step size control is based on the Courant-Friedrichs-Lewy (CFL) number. The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances, while additionally providing control of the temporal error at tighter tolerances. The numerical examples include challenging industrial CFD applications.

A Step Size Control Method Improving Estimation Speed in Double Talk Term

2013 ◽  
Vol E96.A (7) ◽  
pp. 1543-1551 ◽  
Author(s):  
Takuto YOSHIOKA ◽  
Kana YAMASAKI ◽  
Takuya SAWADA ◽  
Kensaku FUJII ◽  
Mitsuji MUNEYASU ◽  
...  
Keyword(s):  
Control Method ◽  
Size Control ◽  
Step Size ◽  
Step Size Control

Continuation Power Flow: a Parameterization Technique and Adaptive Step Size Control

2021 ◽  
Author(s):  
Alfredo Bonini Neto ◽  
Luis Roberto Almeida Gabriel Filho ◽  
Dilson Amancio Alves
Keyword(s):  
Power Flow ◽  
Size Control ◽  
Step Size ◽  
Adaptive Step Size ◽  
Continuation Power Flow ◽  
Step Size Control ◽  
Adaptive Step
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