High-Order Schemes for Navier-Stokes Equations: Algorithm and Implementation Into FDL3DI

1998 ◽  
Author(s):  
Datta V. Gaitonde ◽  
Miguel R. Visbal
Keyword(s):  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
High Order Schemes

scholarly journals Comparison of Higher-Order Numerical Schemes and Several Filtering Methods Applied to Navier-Stokes Equations with Applications to Computational Aeroacoustics

2009 ◽  
Vol 3 (3) ◽  
pp. 443-459
Author(s):  
L.S. Lai ◽  
G.S. Djambazov ◽  
C.-H. Lai ◽  
K.A. Pericleous
Keyword(s):  
Stokes Equations ◽  
Small Time ◽  
High Order ◽  
Navier Stokes ◽  
Acoustic Analogy ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Equations ◽  
High Order Schemes ◽  
Fine Mesh

In computational acoustics, fluid-acoustic coupling methods for the computation of sound have been widely used by researchers for the last five decades. In the first part of the coupling procedure, the fully unsteady incompressible or compressible flow equations for the near-field of the unsteady flow are solved by using a Computational Fluid Dynamics (CFD) technique, such as Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) or unsteady Reynolds averaged Navier-Stokes equations (RANS) the CFD predictions are then used to calculate sound sources using the acoustic analogy or solving a set of acoustic perturbation equations (APE) leading to the solution of the acoustic field. It is possible to use a 2-D reduced problem to provide a preliminary understanding of many acoustic problems. Unfortunately 2-D CFD simulations using a fine-mesh-small-time-step-LES-alike numerical method cannot be considered as LES, which applies to 3-D simulations only. Therefore it is necessary to understand the similarities and the effect between filters applied to unsteady compressible Navier-Stokes equations and the combined effect of high-order schemes and mesh size. The aim of this study is to provide suitable LES-alike methods for 2-D simulations. An efficient software implementation of high-order schemes is also proposed. Numerical examples are provided to illustrate these statistical similarities.

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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