Iterative solution techniques for the stokes and Navier-Stokes equations

1994 ◽  
Vol 19 (1) ◽  
pp. 67-83 ◽  
Author(s):  
Alison Ramage ◽  
Andrew J. Wathen
Keyword(s):  
Stokes Equations ◽  
Iterative Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Solution Techniques

Numerical Modeling of Flow Over a Dam Spillway

2006 ◽  
Author(s):  
Iraj Saeedpanah ◽  
M. Shayanfar ◽  
E. Jabbari ◽  
Mohammad Haji Mohammadi
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Iterative Solution ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Continuity Equations ◽  
Water Jets ◽  
Pressure Fields ◽  
Good Agreement

Free surface flows are frequently encountered in hydraulic engineering problems including water jets, weirs and around gates. An iterative solution to the incompressible two-dimensional vertical steady Navier-Stokes equations, comprising momentum and continuity equations, is used to solve for the priori unknown free surface, the velocity and the pressure fields. The entire water body is covered by a unstructured finite element grid which is locally refined. The dynamic boundary condition is imposed for the free surface where the pressure vanishes. This procedure is done continuously until the normal velocities components vanish. To overcome numerical errors and oscillations encountering in convection terms, the SUPG (streamline upwinding Petrov-Galerkin) method is applied. The solution method is tested for different discharges onto a standard spillway geometries. The results shows good agreement with available experimental data.

scholarly journals Scalable Block Preconditioners for Linearized Navier-Stokes Equations at High Reynolds Number

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 199
Author(s):  
Filippo Zanetti ◽  
Luca Bergamaschi
Keyword(s):  
Stokes Equations ◽  
Schur Complement ◽  
Iterative Solution ◽  
Viscosity Coefficient ◽  
Building Blocks ◽  
Low Rank ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Diffusion Operator ◽  
Advection Diffusion

We review a number of preconditioners for the advection-diffusion operator and for the Schur complement matrix, which, in turn, constitute the building blocks for Constraint and Triangular Preconditioners to accelerate the iterative solution of the discretized and linearized Navier-Stokes equations. An intensive numerical testing is performed onto the driven cavity problem with low values of the viscosity coefficient. We devise an efficient multigrid preconditioner for the advection-diffusion matrix, which, combined with the commuted BFBt Schur complement approximation, and inserted in a 2×2 block preconditioner, provides convergence of the Generalized Minimal Residual (GMRES) method in a number of iteration independent of the meshsize for the lowest values of the viscosity parameter. The low-rank acceleration of such preconditioner is also investigated, showing its great potential.

Numerical Investigations on the Optimum Design of Radial Inflow Turbine Guide Vanes

1994 ◽  
Author(s):  
A. W. Reichert ◽  
H. Simon
Keyword(s):  
High Efficiency ◽  
Stokes Equations ◽  
Guide Vane ◽  
Iterative Solution ◽  
Design Principles ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Guide Vanes ◽  
Standard Interface

To improve the prediction of compressible flow in highly loaded turbomachinery components a modified high resolution scheme to solve the Navier Stokes equations has been developed. The scheme is based on the methods introduced by Osher and Roe. For high efficiency, an implicit iterative solution procedure is used. The code is validated, presenting highly accurate computational results. A structured grid is used during the investigations and a special grid topology for turbine vanes is presented. As the guide vanes are designed using CAD software the CFD code is coupled via the standard interface IGES (Smith et al., 1988). Starting with classical design principles, a first guide vane is designed. Based on flow field computations, the design of the guide vanes is improved successively. Resulting from the experiences gained during the improvement procedure general design principles are formulated.

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