scholarly journals Final Report - High-Order Spectral Volume Method for the Navier-Stokes Equations On Unstructured Tetrahedral Grids

2012 ◽  
Author(s):  
Z J Wang
Keyword(s):  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Final Report ◽  
Navier Stokes Equations ◽  
Spectral Volume ◽  
Tetrahedral Grids ◽  
Volume Method

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.

Improving the High Order Spectral Volume Formulation Using a Diffusion Regulator

2012 ◽  
Vol 12 (1) ◽  
pp. 247-260 ◽  
Author(s):  
Ravi Kannan ◽  
Zhijian Wang
Keyword(s):  
Stokes Equations ◽  
High Order ◽  
High Order Accuracy ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Riemann Solvers ◽  
Flow Problems ◽  
Spectral Volume ◽  
Original Scheme ◽  
New Formulation

AbstractThe concept of diffusion regulation (DR) was originally proposed by Jaisankar for traditional second order finite volume Euler solvers. This was used to decrease the inherent dissipation associated with using approximate Riemann solvers. In this paper, the above concept is extended to the high order spectral volume (SV) method. The DR formulation was used in conjunction with the Rusanov flux to handle the inviscid flux terms. Numerical experiments were conducted to compare and contrast the original and the DR formulations. These experiments demonstrated (i) retention of high order accuracy for the new formulation, (ii) higher fidelity of the DR formulation, when compared to the original scheme for all orders and (iii) straightforward extension to Navier Stokes equations, since the DR does not interfere with the discretization of the viscous fluxes. In general, the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.

NUMERICAL EXPERIMENTS OF THE SPECTRAL VOLUME METHOD FOR VISCOUS FLOWS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1439-1442
Author(s):  
YUZHI SUN ◽  
Z. J. WANG
Keyword(s):  
Numerical Experiments ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Galerkin Approach ◽  
Flow Problems ◽  
Local Discontinuous Galerkin ◽  
Spectral Volume ◽  
Volume Method

In this paper, the spectral volume (SV) method is experimented for the Navier-Stokes equations by treating the viscous terms with a mixed formulation named the local Discontinuous Galerkin approach. The formulation of the SV method for the two-dimensional compressible Navier-Stokes equations is described. The solver is used to solve several viscous flow problems to show its potential.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

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