scholarly journals Optimized Low Dispersion and Low Dissipation Runge-Kutta Algorithms in Computational Aeroacoustics

2014 ◽  
Vol 8 (1) ◽  
pp. 57-68
Author(s):  
Appanah Rao Appadu
Keyword(s):  
Computational Aeroacoustics ◽  
Low Dissipation ◽  
Runge Kutta ◽  
Low Dispersion

scholarly journals The Technique of MIEELDLD in Computational Aeroacoustics

2012 ◽  
Vol 2012 ◽  
pp. 1-30
Author(s):  
A. R. Appadu
Keyword(s):  
Fluid Dynamics ◽  
High Order ◽  
Computational Aeroacoustics ◽  
Advection Equation ◽  
Optimal Parameters ◽  
Numerical Schemes ◽  
Low Dissipation ◽  
Linear Advection Equation ◽  
Discretization Schemes ◽  
Low Dispersion

The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and low dissipation errors. A technique has recently been devised in a Computational Fluid Dynamics framework which enables optimal parameters to be chosen so as to better control the grade and balance of dispersion and dissipation in numerical schemes (Appadu and Dauhoo, 2011; Appadu, 2012a; Appadu, 2012b; Appadu, 2012c). This technique has been baptised as the Minimized Integrated Exponential Error for Low Dispersion and Low Dissipation (MIEELDLD) and has successfully been applied to numerical schemes discretising the 1-D, 2-D, and 3-D advection equations. In this paper, we extend the technique of MIEELDLD to the field of computational aeroacoustics and have been able to construct high-order methods with Low Dispersion and Low Dissipation properties which approximate the 1-D linear advection equation. Modifications to the spatial discretization schemes designed by Tam and Webb (1993), Lockard et al. (1995), Zingg et al. (1996), Zhuang and Chen (2002), and Bogey and Bailly (2004) have been obtained, and also a modification to the temporal scheme developed by Tam et al. (1993) has been obtained. These novel methods obtained using MIEELDLD have in general better dispersive properties as compared to the existing optimised methods.

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 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 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.

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