Some new exact solutions for the two-dimensional Navier–Stokes equations

2007 ◽  
Vol 371 (5-6) ◽  
pp. 438-452 ◽  
Author(s):  
Chiping Wu ◽  
Zhongzhen Ji ◽  
Yongxing Zhang ◽  
Jianzhong Hao ◽  
Xuan Jin
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
New Exact Solutions

New Exact Axisymmetric Solutions to the Navier–Stokes Equations

2019 ◽  
Vol 75 (1) ◽  
pp. 29-42
Author(s):  
Oleg Bogoyavlenskij
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Dimensional Space ◽  
Phase Portraits ◽  
Navier Stokes ◽  
Elementary Functions ◽  
Navier Stokes Equations ◽  
New Exact Solutions ◽  
Whole Space ◽  
Dependent Viscosity

AbstractInfinite-dimensional space of axisymmetric exact solutions to the Navier–Stokes equations with time-dependent viscosity $\nu(t)$ is constructed. Inner transformations of the exact solutions are defined that produce an infinite sequence of new solutions from each known one. The solutions are analytic in the whole space ℝ3 and are described by elementary functions. The bifurcations of the instantaneous (for $t={t_{0}}$) phase portraits of the viscous fluid flows are studied for the new exact solutions. Backlund transforms between the axisymmetric Helmholtz equation and a linear case of the Grad–Shafranov equation are derived.

Laminar Flow Between Two Parallel Porous Walls With Variable Permeability and Wall Slip

2002 ◽  
Author(s):  
S. Krishnambal
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Wall Slip ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Variable Permeability ◽  
Stream Lines ◽  
Variable Suction

A class of exact solutions of two dimensional Navier-Stokes equations representing the flow between two porous parallel walls, when there exist variable suction and injection at the boundaries (with or with out slip) under the prescribed entry and outlet conditions at the ends of the channel of given length is obtained. These are exact solutions of the two dimensional Navier-Stokes equations for a suitable class of variable suction and injection prescribed at the walls. Certain interesting flow characteristics are observed, when analysed through the graphs of velocity profiles and stream lines. The change in the pattern of the stream lines corresponding to the various prescribed suction/injection velocities are observed. The convergence analysis (with slip) of the series solution is discussed with a suitable numerical example.

Sign in / Sign up

Export Citation Format

Share Document