Low-Dissipation and Low-Dispersion Runge–Kutta Schemes for Computational Acoustics

1996 ◽  
Vol 124 (1) ◽  
pp. 177-191 ◽  
Author(s):  
F.Q. Hu ◽  
M.Y. Hussaini ◽  
J.L. Manthey
Keyword(s):  
Low Dissipation ◽  
Runge Kutta ◽  
Low Dispersion

Low-dissipation and low-dispersion fourth-order Runge–Kutta algorithm

2006 ◽  
Vol 35 (10) ◽  
pp. 1459-1463 ◽  
Author(s):  
Julien Berland ◽  
Christophe Bogey ◽  
Christophe Bailly
Keyword(s):  
Fourth Order ◽  
Low Dissipation ◽  
Runge Kutta ◽  
Low Dispersion

Low-dissipation low-dispersion explicit Taylor-Galerkin schemes from the Runge-Kutta kernels

2018 ◽  
Vol 17 (1-2) ◽  
pp. 88-113
Author(s):  
Mostafa Najafiyazdi ◽  
Luc Mongeau ◽  
Siva Nadarajah
Keyword(s):  
Time Integration ◽  
Second Order ◽  
Order Of Accuracy ◽  
Galerkin Scheme ◽  
Integration Schemes ◽  
Low Dissipation ◽  
Multi Stage ◽  
Time Integration Schemes ◽  
Runge Kutta ◽  
Low Dispersion

A multi-stage approach was adopted to investigate similarities and differences between the explicit Taylor-Galerkin and the explicit Runge-Kutta time integration schemes. It was found that the substitution of some, but not all, of second-order temporal derivatives in a Taylor-Galerkin scheme by additional stages makes it analogous to a Runge-Kutta scheme while preserving its original dissipative property for node-to-node oscillations. The substitution of all second-order temporal derivatives transforms Taylor-Galerkin schemes into Runge-Kutta schemes with zero attenuation at the grid cut-off. The application of this approach to an existing two-stage Taylor-Galerkin scheme yields a low-dissipation low-dispersion Taylor-Galerkin formulation. Two one-dimensional benchmarks were simulated to study the performance of this new scheme. The reverse process yields a general approach for transforming m-stage Runge-Kutta schemes into ( m−1)-stage Taylor-Galerkin schemes while preserving the same order of accuracy. The dissipation and dispersion properties for several new Taylor-Galerkin schemes were compared to those of their corresponding Runge-Kutta form.

High-order low-dissipation low-dispersion diagonally implicit Runge–Kutta schemes

2015 ◽  
Vol 286 ◽  
pp. 38-48 ◽  
Author(s):  
Farshid Nazari ◽  
Abdolmajid Mohammadian ◽  
Martin Charron
Keyword(s):  
High Order ◽  
Low Dissipation ◽  
Runge Kutta ◽  
Low Dispersion
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