## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2019 (2019), Article ID 3084394, 19 pages.

### A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

Abdul-Sattar J. Al-Saif and Assma J. Harfash

#### Abstract

In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers.

#### Article information

**Source**

J. Appl. Math., Volume 2019 (2019), Article ID 3084394, 19 pages.

**Dates**

Received: 13 October 2018

Accepted: 9 December 2018

First available in Project Euclid: 26 February 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1551150320

**Digital Object Identifier**

doi:10.1155/2019/3084394

**Mathematical Reviews number (MathSciNet)**

MR3898788

#### Citation

Al-Saif, Abdul-Sattar J.; Harfash, Assma J. A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations. J. Appl. Math. 2019 (2019), Article ID 3084394, 19 pages. doi:10.1155/2019/3084394. https://projecteuclid.org/euclid.jam/1551150320