scholarly journals Development of openfoam solvers for incompressible navier–stokes equations based on high-order runge–kutta schemes

2016 ◽  
Vol 4 (4) ◽  
pp. 594-603 ◽  
Author(s):  
V. D’Alessandro ◽  
A. Zoppi ◽  
L. Binci ◽  
R. Ricci
Keyword(s):  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Runge Kutta

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part I: Implicit Runge–Kutta Schemes

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Graham Ashcroft ◽  
Christian Frey ◽  
Kathrin Heitkamp ◽  
Christian Weckmüller
Keyword(s):  
Stokes Equations ◽  
Temporal Integration ◽  
Aerodynamic Noise ◽  
Navier Stokes ◽  
Noise Generation ◽  
Academic Problems ◽  
Tonal Noise ◽  
Navier Stokes Equations ◽  
Runge Kutta ◽  
The Stability

This is the first part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. In this part, the stability, accuracy, and efficiency of implicit Runge–Kutta schemes for the temporal integration of the compressible Navier–Stokes equations are investigated in the context of a CFD code for turbomachinery applications. Using two model academic problems, the properties of two explicit first stage, singly diagonally implicit Runge–Kutta (ESDIRK) schemes of second- and third-order accuracy are quantified and compared with more conventional second-order multistep methods. Finally, to assess the ESDIRK schemes in the context of an industrially relevant configuration, the schemes are applied to predict the tonal noise generation and transmission in a modern high bypass ratio fan stage and comparisons with the corresponding experimental data are provided.

Implicit High-Order-Accurate-in-Space Algorithms for the Navier-Stokes Equations

AIAA Journal ◽  
2000 ◽  
Vol 38 (9) ◽  
pp. 1594-1602 ◽  
Author(s):  
John A. Ekaterinaris
Keyword(s):  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equations
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