Analysis and application of high order implicit Runge–Kutta schemes to collocated finite volume discretization of the incompressible Navier–Stokes equations

2015 ◽  
Vol 108 ◽  
pp. 107-115 ◽  
Author(s):  
V. Kazemi-Kamyab ◽  
A.H. van Zuijlen ◽  
H. Bijl
Keyword(s):  
Finite Volume ◽  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Volume Discretization ◽  
Runge Kutta

A Hybrid Unstructured/Spectral Method for the Resolution of Navier-Stokes Equations

2009 ◽  
Author(s):  
Roque Corral ◽  
Javier Crespo
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
The Third ◽  
Third Dimension ◽  
Volume Method

A novel high-order finite volume method for the resolution of the Navier-Stokes equations is presented. The approach combines a third order finite volume method in an unstructured two-dimensional grid, with a spectral approximation in the third dimension. The method is suitable for the resolution of complex two-dimensional geometries that require the third dimension to capture three-dimensional non-linear unsteady effects, such as those for instance present in linear cascades with separated bubbles. Its main advantage is the reduction in the computational cost, for a given accuracy, with respect standard finite volume methods due to the inexpensive high-order discretization that may be obtained in the third direction using fast Fourier transforms. The method has been applied to the resolution of transitional bubbles in flat plates with adverse pressure gradients and realistic two-dimensional airfoils.

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