A CLASS OF EXACT SOLUTION TO THE THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
An exact solution of the three-dimensional incompressible Navier-Stokes equations with the continuity equation is produced in this work. The solution is proposed to be in the form where is a potential function that is defined as , with the application of the transformed coordinate . The potent...
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| Main Authors: | , , |
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| Format: | Article |
| Published: |
2010
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| Subjects: | |
| Online Access: | http://eprints.utp.edu.my/6236/1/A_Class_of_Exact_Solution_to_the_Three-Dimensional_Incompressible_Navier-Stokes_Equations_%28080609%29.pdf http://eprints.utp.edu.my/6236/ |
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| Institution: | Universiti Teknologi Petronas |
| Summary: | An exact solution of the three-dimensional incompressible Navier-Stokes equations with the continuity equation is produced in this work. The solution is proposed to be in the form where is a potential function that is defined as , with the application of the transformed coordinate . The potential function is firstly substituted into the continuity equation to produce the solution for and . The resultant expression is used sequentially in the Navier-Stokes equations to reduce the problem to the class of nonlinear ordinary differential equations in terms, in which the pressure term is presented in a general functional form. General solutions are obtained based on the particular solutions of where the equation is reduced to the form of linear differential equation. A method for finding closed-form solutions for general linear differential equations is also proposed. |
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