Runge–Kutta time-stepping schemes with TVD central differencing for the water hammer equations

2006 ◽  
Vol 52 (5) ◽  
pp. 571-590 ◽  
Author(s):  
E. M. Wahba
Keyword(s):  
Water Hammer ◽  
Time Stepping ◽  
Runge Kutta

scholarly journals Multigrid and Runge-Kutta time stepping applied to the uniformly non-oscillatory scheme for conservation laws

1991 ◽  
Vol 25 (3) ◽  
pp. 243-263 ◽  
Author(s):  
J. W. van der Burg ◽  
J. G. M. Kuerten ◽  
P. J. Zandbergen
Keyword(s):  
Conservation Laws ◽  
Time Stepping ◽  
Runge Kutta

Runge--Kutta-Based Explicit Local Time-Stepping Methods for Wave Propagation

2015 ◽  
Vol 37 (2) ◽  
pp. A747-A775 ◽  
Author(s):  
Marcus J. Grote ◽  
Michaela Mehlin ◽  
Teodora Mitkova
Keyword(s):  
Wave Propagation ◽  
Local Time ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Runge Kutta

scholarly journals A framework to evaluate IMEX schemes for atmospheric models

2020 ◽  
Vol 13 (12) ◽  
pp. 6467-6480
Author(s):  
Oksana Guba ◽  
Mark A. Taylor ◽  
Andrew M. Bradley ◽  
Peter A. Bosler ◽  
Andrew Steyer
Keyword(s):  
Acoustic Waves ◽  
Normal Modes ◽  
Evaluation Framework ◽  
Acoustic System ◽  
Time Stepping ◽  
Imex Schemes ◽  
Runge Kutta ◽  
The Stability ◽  
Implicit And Explicit ◽  
New Framework

Abstract. We present a new evaluation framework for implicit and explicit (IMEX) Runge–Kutta time-stepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes. We utilize the framework to investigate the stability of IMEX methods and their dispersion and dissipation of gravity, Rossby, and acoustic waves. We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of second-order low-storage IMEX Runge–Kutta methods with a high Courant–Friedrichs–Lewy (CFL) number. We show that the new framework is more selective than the 2-D acoustic system previously used in the literature. Schemes that are stable for the 2-D acoustic system are not stable for the system of normal modes.

scholarly journals Efficient extrapolation methods for electro- and magnetoquasistatic field simulations

2003 ◽  
Vol 1 ◽  
pp. 81-86 ◽  
Author(s):  
M. Clemens ◽  
M. Wilke ◽  
T. Weiland
Keyword(s):  
Taylor Series Expansion ◽  
Iterative Solvers ◽  
Gradient Algorithm ◽  
Implicit Time ◽  
Preconditioned Conjugate Gradient ◽  
Test Problems ◽  
Time Step ◽  
Time Stepping ◽  
Multi Stage ◽  
Runge Kutta

Abstract. In magneto- and electroquasi-static time domain simulations with implicit time stepping schemes the iterative solvers applied to the large sparse (non-)linear systems of equations are observed to converge faster if more accurate start solutions are available. Different extrapolation techniques for such new time step solutions are compared in combination with the preconditioned conjugate gradient algorithm. Simple extrapolation schemes based on Taylor series expansion are used as well as schemes derived especially for multi-stage implicit Runge-Kutta time stepping methods. With several initial guesses available, a new subspace projection extrapolation technique is proven to produce an optimal initial value vector. Numerical tests show the resulting improvements in terms of computational efficiency for several test problems. In quasistatischen elektromagnetischen Zeitbereichsimulationen mit impliziten Zeitschrittverfahren zeigt sich, dass die iterativen Lösungsverfahren für die großen dünnbesetzten (nicht-)linearen Gleichungssysteme schneller konvergieren, wenn genauere Startlösungen vorgegeben werden. Verschiedene Extrapolationstechniken werden für jeweils neue Zeitschrittlösungen in Verbindung mit dem präkonditionierten Konjugierte Gradientenverfahren vorgestellt. Einfache Extrapolationsverfahren basierend auf Taylorreihenentwicklungen werden ebenso benutzt wie speziell für mehrstufige implizite Runge-Kutta-Verfahren entwickelte Verfahren. Sind verschiedene Startlösungen verfügbar, so erlaubt ein neues Unterraum-Projektion- Extrapolationsverfahren die Konstruktion eines optimalen neuen Startvektors. Numerische Tests zeigen die aus diesen Verfahren resultierenden Verbesserungen der numerischen Effizienz.

Optimal embedded pair Runge-Kutta schemes for pseudo-time stepping

2020 ◽  
Vol 415 ◽  
pp. 109499
Author(s):  
Brian C. Vermeire ◽  
Niki A. Loppi ◽  
Peter E. Vincent
Keyword(s):  
Time Stepping ◽  
Runge Kutta
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