scholarly journals Numerical Simulation of Two-Dimensional Natural Convection in a Confined Environment with the Vorticity-Stream Function Formulation

2018 ◽  
Vol 08 (01) ◽  
pp. 44-58
Author(s):  
Mame Khady Kane ◽  
Cheikh Mbow ◽  
Mamadou Lamine Sow ◽  
Joseph Sarr
Keyword(s):  
Numerical Simulation ◽  
Natural Convection ◽  
Stream Function ◽  
Two Dimensional ◽  
Function Formulation ◽  
Stream Function Formulation ◽  
Confined Environment

scholarly journals Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Mohamed A. El-Beltagy ◽  
Mohamed I. Wafa
Keyword(s):  
Stream Function ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Function Formulation ◽  
Mean And Variance ◽  
The Mean ◽  
Stream Function Formulation

A two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. A second-order upwind scheme is used in the convection term for numerical stability and higher-order discretization. The resulting sparse linear system is solved efficiently by a direct parallel solver. The mean and variance simulations of the cavity flow are done for random variation of the viscosity and the lid velocity. The solver was tested and compared with the Monte-Carlo simulations and with previous research works. The developed solver is proved to be efficient in simulating the stochastic two-dimensional incompressible flows.

scholarly journals A numerical investigation of a buoyancy driven flow in a semi-porous cavity: comparative effects of ramped and isothermal wall conditions

2013 ◽  
Vol 61 (2) ◽  
pp. 103-111 ◽  
Author(s):  
Pallath Chandran ◽  
Nirmal C. Sacheti ◽  
Ashok K. Singh
Keyword(s):  
Natural Convection ◽  
Temperature Distribution ◽  
Nonlinear Partial Differential Equations ◽  
Darcy Number ◽  
Two Dimensional ◽  
Function Formulation ◽  
Isotropic Porous Material ◽  
Vertical Walls ◽  
Isothermal Wall ◽  
Stream Function Formulation

Abstract Steady two-dimensional natural convection taking place in a rectangular cavity, partially filled with an isotropic porous material, has been investigated numerically using an ADI method. It is assumed that one of the vertical walls of the cavity has a ramped temperature distribution. The vorticity-stream function formulation has been used to solve the set of nonlinear partial differential equations governing the flows in the clear region and the adjoining porous region. The effects of Darcy number and Rayleigh number have been discussed in detail.

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