Generation and solutions to the time-space fractional coupled Navier-Stokes equations

• Main Authors: Lu Chang-Na, Chang Sheng-Xiang, Xie Luo-Yan, Zhang Zong-Guo
• Format: Article
• Language: English
• Published: VINCA Institute of Nuclear Sciences 2020-01-01
• Series: Thermal Science
• Subjects: time-space fractional coupled navier-stokes equations; agrawal’s method; residual power series method; fractional derivatives
• Online Access: http://www.doiserbia.nb.rs/img/doi/0354-9836/2020/0354-98362006899L.pdf

In this paper, a Lagrangian of the coupled Navier-Stokes equations is proposed based on the semi-inverse method. The fractional derivatives in the sense of Riemann-Liouville definition are used to replace the classical derivatives in the Lagrangian. Then the fractional Euler-Lagrange equation can be derived with the help of the fractional variational principles. The Agrawal’s method is devot­ed to lead to the time-space fractional coupled Navier-Stokes equations from the above Euler-Lagrange equation. The solution of the time-space fractional coupled Navier-Stokes equations is obtained by means of RPS algorithm. The numerical results are presented by using exact solutions.