Steady-state solution of incompressible Navier-Stokes equations using discrete least-squares meshless method

2010 ◽  
Vol 67 (3) ◽  
pp. 369-382 ◽  
Author(s):  
Ali Rahmani Firoozjaee ◽  
Mohammad Hadi Afshar
Keyword(s):  
Steady State ◽  
Least Squares ◽  
Meshless Method ◽  
Stokes Equations ◽  
Steady State Solution ◽  
State Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations

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.

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