scholarly journals A multigrid finite volume method for solving the Euler and Navier-Stokes equations for high speed flows

1989 ◽  
Author(s):  
M. SICLARI ◽  
P. DELGUIDICE ◽  
A. JAMESON
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
High Speed ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
High Speed Flows

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.

Numerical Calculation on Vortex-Induced Vibration of the Circular Cylinder Using Low Reynolds Model in Hybrid Method

2009 ◽  
Author(s):  
Xingwei Zhang ◽  
Chaoying Zhou
Keyword(s):  
Numerical Calculation ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Mesh Method ◽  
Volume Method

Fundamental research on interaction between flow and structure is presented for computation the fluid dynamics of different two-dimensional oscillating models. The Navier-Stokes equations are solved using finite volume method. A multigrid mesh method which was applied to the situation of flow past the stagnating or vibrating cylinder is developed to simulate this type of flow. The interactive results between flow and structure rigid cylinders have been present. The computation fluid dynamic codes mainly with low Reynolds RANS solver are used to solve the impressible viscous Navier-Stokes equations. Finite volume method which is coupled with conformal hybrid mesh method is developed to simulate this type of flow. Numerical investigation focused on the response and the fluid forces on the cylinders and also observed the different shedding model in the wake. The numerical results are compared in detail with recent experimental and computational work. Present numerical comparison also showed that solution using different turbulence model will make the result have a little discrepancy and each turbulence model has respective characteristics in numerical solution on the vortex-induced vibration of the cylinder. In addition, the formation of the 2P vortex shedding model through the lock-in region and the beginning of the shedding model transformation in numerical calculation from 2S model to 2P model has been analyzed.

Block-preconditioners for the incompressible Navier–Stokes equations discretized by a finite volume method

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Xin He ◽  
Cornelis Vuik ◽  
Christiaan Klaij
Keyword(s):  
Reynolds Number ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Augmented Lagrangian ◽  
Dimensionless Parameter ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Optimal Value ◽  
Volume Method

Abstract The modified augmented Lagrangian preconditioner has attracted much attention in solving nondimensional Navier–Stokes equations discretized by the finite element method. In industrial applications the governing equations are often in dimensional form and discretized using the finite volume method. This paper assesses the capability of this preconditioner for dimensional Navier–Stokes equations in the context of the finite volume method. Two main contributions are made. First, this paper introduces a new dimensionless parameter that is involved in the modified augmented Lagrangian preconditioner. Second, with a number of academic test problems this paper reveals that the convergence of both nonlinear and linear iterations depend on this dimensionless parameter. A way to choose the optimal value of the dimensionless parameter is suggested and it is found that the optimal value is dependent of the Reynolds number, instead of the fluid’s properties, e.g., density and dynamic viscosity. The outcomes of this paper yield a potential rule to choose the optimal dimensionless parameter in practice, namely, correspondingly increasing with enlarging the Reynolds number.

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