Locally one-dimensional difference scheme for the convective diffusion equation

1994 ◽  
Vol 72 (2) ◽  
pp. 3021-3024 ◽  
Author(s):  
D. A. Bugai
Keyword(s):  
Diffusion Equation ◽  
Difference Scheme ◽  
Convective Diffusion ◽  
One Dimensional ◽  
Convective Diffusion Equation

Numerical Solution to the Convective Diffusion Equation

1970 ◽  
Vol 6 (6) ◽  
pp. 1746-1752 ◽  
Author(s):  
C. A. Oster ◽  
J. C. Sonnichsen ◽  
R. T. Jaske
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Convective Diffusion ◽  
Convective Diffusion Equation

scholarly journals Solutions of Navier-Stokes Equation with Coriolis Force

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Sunggeun Lee ◽  
Shin-Kun Ryi ◽  
Hankwon Lim
Keyword(s):  
Diffusion Equation ◽  
Stokes Equation ◽  
Coriolis Force ◽  
Potential Flow ◽  
Convective Diffusion ◽  
Navier Stokes ◽  
Coriolis Effect ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Convective Diffusion Equation

We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.

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