Convection and diffusion

1
Convection and diffusion

• assume a known flow field
• generalize T and k as
• F and G

continuity and momentum equations
2
Steady1D convection and diffusion
convective- diffusion equation
continuity
3
Discretization using central differences
central difference scheme
4
Discretization using central differences
5
Discretization using upwinding
central difference scheme
upwind scheme
6
Discretization using upwinding
meaning the greater of A and B
define a new operator
then
7
Discretization using upwinding
8
Exact solution
1D convective-diffusion equation
given simple boundary conditions
has an exact solution
where the Peclet number is
9
Exact solution and the Peclet number