Science Journal of Physics

March 2013, Volume 2013, ISSN:2276-6367

Author(s) 2013. This work is distributed under the Creative Commons Attribution 3.0 License.

Research Article


Unique Numerical Scheme for a Modified Equation of Fluid Motion: Approaching New Solver Development to a Fundamental Flow Problem

Author: Bo Wan*, Friedrich Karl Benra and Hans Josef Dohmen

Department of Mechanical Engineering, Faculty of Engineering Sciences University of Duisburg-Essen Keetmanstr.
3-9, 47058 Duisburg, GERMANY
Tel: 0049-203-379-3013 Fax: 0049-203-379-3038

Accepted 21 January 2013; Available Online 13 March 2013

doi: 10.7237/sjp/231


On the basis of a scale-invariant model of statistical mechanics, the scale-invariant form of the equation of motion was introduced by Sohrab recently. This newly modified equation of fluid motion owns linear properties and is almost identical to the classical Navier-Stokes equations for solving flow problems. In order to dig potential advantages of this modified equation in engineering applications, the current paper goes deeper insights into the modified equation of fluid motion by the numerical method. In Open FOAM environment, a numerical solver was developed to employ this modified equation to solve engineering flow problems. After the finite volume method discretisation was carried out, the resulted algebraic equations derived from the modified equation were linear. Hence another technique was assigned to the developed solver to improve the iteration procedure. As an application example, the laminar boundary layer flow over a flat plate was resolved by the developed solver. Comparing the obtained results with those of the Navier-Stokes solver and measurement, it is found that the developed solver produced reasonable predictions for this fundamental flow problem, and consumed much less computational time than the Navier-Stokes due to the linear properties. Such results conclude that the developed solver is more efficient than the current ones solving the Navier-Stokes equations.

Keywords:Modified Equation of Fluid Motion, Statistical Mechanics, CFD, Navier-Stokes Equations, Flat Plate