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A Finite Volume Solution of Unsteady Incompressible Navier-Stokes Equations Using MATLAB |
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PP: 117-131 |
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Author(s) |
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Endalew Getnet Tsega,
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Abstract |
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| Navier-Stokes equations which represent the momentum conservation of an incompressible Newtonian fluid flow are the fundamental governing equations in fluid dynamics. For real fluid flow situations, the equations are too difficult to solve analytically except for very simplified cases. A formal uniqueness and existence of the solutions has not been established using mathematical analysis. Nowadays, high speed and large memory computers have been used to solve the Navier-Stokes equations approximately together with continuity equations using a variety of numerical techniques. In this study, a finite volume technique is used to solve the Navier-Stokes equations for unsteady flow of Newtonian incompressible fluid with no body forces using MATLAB. The method is implemented on unsteady internal fluid flow in a 2D straight channel. The equations are solved to obtain velocity and pressure fields on staggered grid. The x and y velocity components are recomputed together at new locations to determine the resultant velocity at those locations. The computed velocity and pressure values using the solution method show a good agreement with that of the commercial CFD software, ANSYS Fluent. The solution method provides a possible alternative for handling resultant velocity and implementation of boundary conditions in discretization method by staggered grid. The result of this study can help users to write their own codes and use commercial CFD codes proficiently in solving equations of fluid flow using numerical discretization schemes. |
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