scholarly journals Stability analysis of Galerkin/Runge-Kutta Navier-Stokes discretisations on unstructured grids

1995 ◽  
Author(s):  
M Giles
Keyword(s):  
Stability Analysis ◽  
Unstructured Grids ◽  
Navier Stokes ◽  
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.

Spatial Stability Analysis of a Flap Side Edge Vortex

2005 ◽  
Vol 4 (1-2) ◽  
pp. 37-47
Author(s):  
Jean-Philippe Brazier ◽  
Frédéric Moens ◽  
Philippe Bardoux
Keyword(s):  
Stability Analysis ◽  
Temporal Stability ◽  
Low Frequency ◽  
Aerodynamic Noise ◽  
Navier Stokes ◽  
Mean Flow ◽  
Side Edge ◽  
Amplification Rate ◽  
Edge Vortex ◽  
Flap Deflection

The flap side edge vortex is suspected to contribute to aerodynamic noise generation. Using a temporal stability analysis, Khorrami and Singer have shown that unstable modes could exist in this vortex. Due to the convective nature of this instability, a spatial analysis is more suitable. This is the subject of the present work. The mean flow past a 2D wing with a half-span flap has been computed with a steady 3D Navier-Stokes code. Then, local linear stability calculations are performed in several planes perpendicular to the vortex axis. The vortex is assumed axisymmetric and modelled with Batchelor's analytical vortex. Using Gaster's relation, the spatial amplification rate is calculated, giving by integration the relative amplitude of the fluctuations. Some low-frequency fluctuations are seen to be preferentially amplified by the vortex, but the amplifications remain small, so that this mechanism alone should not produce important noise in this particular configuration, where the flap deflection angle is moderate.

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