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Simulation for Natural Convection of Fluid Flow Numerically (Upwind Difference - Differential Quadature Method)
The new method is developing to the issue of differential qadrature method (DQM) by entering the upwind mechanism on convection terms and using splitting scheme.
By Abdul-Sattar Jaber Al-Saif
Oct. 6, 2015

The fluid flow problems are very interest and have many applications and wide uses in the area of applied sciences such as, physics, engineering, Biological, ... ect. The nonlinear behavior of fluid flow and effected of varying temperature at heated plate in solid-body rotation and/or an enclosure rectangular box are emphasized in the present study. These kinds of problems are possible great complexity involving many physical effects (or other sciences) and a considerable set of non-linear equations. So, almost they haven't exact solution and need numerical methods to solve it. Here by proposal a new methodology for differential quadrature method these problems are simulated to examine the effects of a heated on natural convection of fluid flow.The application of a new numerical method with a few grid points appears that it has better convergence and accuracy than the other methods in literature.

This subject has been studied extensively by many investigators, in differs situations. The underlying techniques for solve numerically these problems can be very complex and require a large amount of computational time to obtain accurate and reasonable stable solutions. This is certainly due to the difficulties to model such flows: the heat transfer equation can be quite complex, as well as its coupling with momentum equations. According to these reasons, and the lack information on the solution of natural convection heat transfer fluid flow by differential quadrature motivates to the present work. The Schematic diagram of the test regions (solid-body rotation and an enclosure rectangular box) of natural convection of fluid flow problems can be described in the following Figures.

(a)

(b)

Fig.1 Diagram of the test region (a) solid-body rotation (b)an enclosure rectangular box

In this study extending the application of our new method that improved DQM by using upwind mechanism with splitting scheme for solving two-dimensional steady and unsteady state fluid flow problems are introduced. Results show that the convergence of the new method is faster and the solutions have high accuracy, good convergence, reasonable stability and less computation workload.

A paper about this study has been published in the Science Publishing Group/Journal name: Applied and Computational Mathematics.

Here is the paper link:
http://www.sciencepublishinggroup.com/journal/paperinfo.aspx?journalid=147&doi=10.11648/j.acm.20150404.16

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