Bifurcations of a Steady-State Solution to the Two-Dimensional Navier-Stokes Equations

1999 ◽  
Vol 201 (1) ◽  
pp. 117-138 ◽  
Author(s):  
Zhi-Min Chen
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Steady State Solution ◽  
State Solution ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations

Navier-Stokes Computation of Radial Inflow Turbine Distributor

1988 ◽  
Vol 110 (1) ◽  
pp. 29-32 ◽  
Author(s):  
T. C. Vu ◽  
W. Shyy
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Energy Loss ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Two Dimensional Flow ◽  
Radial Inflow Turbine

A two-dimensional flow analysis of a radial inflow turbine distributor using full steady-state Reynolds-averaged Navier-Stokes equations is made. The numerical prediction of the total energy loss and the wicket gate torque is compared with experimental data. Also, a parametric study is carried out in order to evaluate the behavior of the numerical algorithm.

On the Use of the Fully Compressible Navier-Stokes Equations for the Steady-State Solution of Natural Convection Problems in Closed Cavities

2006 ◽  
Vol 129 (3) ◽  
pp. 387-390 ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Pressure Rise ◽  
Steady State Solution ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Simple Strategy ◽  
Reference Pressure

The steady-state compressible form of the Navier-Stokes equations, along with no-slip boundary conditions on walls, represents a boundary value problem. In closed heated cavities, these equations are incapable of preserving the initial mass of the cavity and predicting the pressure rise. A simple strategy to adjust the reference pressure in the system is presented and demonstrated. The strategy is similar to solving the transient form of the governing equations, but completely eliminates truncation errors associated with temporal discretization of the transient terms. Results exhibit good agreement with previous reports. Additional results are shown to highlight differences between the fully compressible formulation and the Boussinesq approximation.

Steady-state analytical solutions for the lattice boltzmann equation

Open Physics ◽  
2003 ◽  
Vol 1 (3) ◽  
Author(s):  
Gábor Házi
Keyword(s):  
Steady State ◽  
Boltzmann Equation ◽  
Analytical Solutions ◽  
Poiseuille Flow ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lattice Boltzmann Equation ◽  
Two Dimensional ◽  
Navier Stokes Equations

AbstractA general class of analytical solutions of the lattice Boltzmann equation is derived for two-dimensional, steady-state unidirectional flows. A subset of the solutions that verifies the corresponding Navier-Stokes equations is given. It is pointed out that this class includes, e.g., the Couette and the Poiseuille flow but not, e.g., the basic Kolmogorov flow. For steady-state non-unidirectional flows, first and second order solutions of the lattice Boltzmann equation are derived. Practical consequences of the analysis are mentioned. Differences between the technique applied here and those used in some earlier works are emphasized.

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