Explicit Exponential Finite Difference Scheme for 1D Navier-Stokes Equation with Time Dependent Pressure Gradient

Authors

  • MAK Azad Department of Mathematics, Shaheed Begum Sheikh Fazilatun Nessa Mujib Govt. College,Dhaka
  • LS Andallah Department of Mathematics, Jahangirnagar University, Savar, Dhaka

DOI:

https://doi.org/10.3329/ganit.v36i0.32775

Keywords:

Navier-Stokes equation, Burgers’ equation, Explicit exponential finite difference scheme

Abstract

In this paper, numerical technique for solving the one-dimensional (1D) unsteady, incompressible Navier-Stokes equation (NSE) is presented. The governing time dependent non-linear partial equation is reduced to non-linear partial differential equation named as viscous Burgers equation by introducing Orlowski and Sobczyk transformation (OST). An explicit exponential finite difference scheme (Expo FDS) has been used for solving reduced 1D NSE. The accuracy of the method has been illustrated by taking two numerical examples. Results are compared with the analytical solutions and those obtained based on the numerical results of reduced 1D NSE as Burgers equation. The accuracy and numerical feature of convergence of the Expo FDS is presented by estimating their error norms. Excellent numerical results indicate that the proposed numerical technique is efficient admissible with efficient accuracy for the numerical solutions of the NSE.

GANIT J. Bangladesh Math. Soc.Vol. 36 (2016) 79-90

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Author Biography

MAK Azad, Department of Mathematics, Shaheed Begum Sheikh Fazilatun Nessa Mujib Govt. College,Dhaka



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Published

2017-06-03

How to Cite

Azad, M., & Andallah, L. (2017). Explicit Exponential Finite Difference Scheme for 1D Navier-Stokes Equation with Time Dependent Pressure Gradient. GANIT: Journal of Bangladesh Mathematical Society, 36, 79–90. https://doi.org/10.3329/ganit.v36i0.32775

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