Abstract
This paper summarizes several new developments in the theory of high-order implicit Runge-Kutta (RK) methods based on generalized summation-by-parts (GSBP) operators. The theory is applied to the construction of several known and novel Runge-Kutta schemes. This includes the well-known families of fully-implicit Radau IA/IIA and Lobatto IIIC Runge-Kutta methods. In addition, a novel family of GSBP-RK schemes based on Gauss quadrature rules is presented along with a few optimized diagonally-implicit GSBP-RK schemes. The novel schemes are all L-stable and algebraically stable. The stability and relative efficiency of the schemes is investigated with numerical simulation of the linear convection equation with both time-independent and time-dependent convection velocities. The numerical comparison includes a few popular non-GSBP Runge-Kutta time-marching methods for reference.
| Original language | English |
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| Title of host publication | 22nd AIAA Computational Fluid Dynamics Conference |
| Publisher | American Institute of Aeronautics and Astronautics Inc, AIAA |
| ISBN (Print) | 9781624103667 |
| DOIs | |
| State | Published - 2015 |
| Externally published | Yes |
| Event | 22nd AIAA Computational Fluid Dynamics Conference, 2015 - Dallas, United States Duration: 22 Jun 2015 → 26 Jun 2015 |
Publication series
| Name | 22nd AIAA Computational Fluid Dynamics Conference |
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Conference
| Conference | 22nd AIAA Computational Fluid Dynamics Conference, 2015 |
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| Country/Territory | United States |
| City | Dallas |
| Period | 22/06/15 → 26/06/15 |
Bibliographical note
Publisher Copyright:© 2015, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.
ASJC Scopus subject areas
- Fluid Flow and Transfer Processes
- Mechanical Engineering