I am solving a transinet convection-diffusion equation
u_t + a*u_x - nu*u_xx = 0 in (0,1)
Taking,
Convection coefficient a = 1
Diffusion coefficient nu = 0.005
Number of elements = 100
I got Peclet number Pe = 1
For same case now,
Time step = 0.01
End time = 0.6
I got Courant number C = 1
I need following 4 conditions to fulfill.
1). C =1 and Pe = 5
2). C =1 and Pe = 100
3). C =3 and Pe = 5
4). C =3 and Pe = 100
My question is:
What should be the value of
"Convection coefficient a",
"Number of elements",
"Diffusion coefficient nu",
"Time step" and
"End time"
to get these 4 results separately.
CFL=U*delta t/delta x. you should measure the minimum size of your grid as the delta x. U is the mean value for flow. For a stable solution, the courant number should be equal or less than 1. Then you can chose your time step.
Dear Muhammad Bilal Ghaffar,
Peclet number relates mainly to spatial discretization, while Courant number to temporal discretization.
Courant number: The Courant number is defined as Cr= epsilon Dt/h
Diffusion number: The diffusion number is defined as S=gama Dt/(h*h)
Grid Péclet number: The Péclet number is defined as Pe = Cr/S .
They are used in Advection Diffusion Equation.When the Péclet number is high, the convection term dominates and when the Péclet number is low the diffusion term.
The Courant number reflects the importance of the convection process, the grid Peclet and Courant numbers can be respectively defined as t 1 do Pe(h) = BA. The values of these parameters are generally higher for coarser materials. For 3D transport models, the main problem is the large CPU time demand because all known finite difference and finite element algorithms have to take into account the grid Peclet number and Courant number limits.
Co = J^ _ < (0.5... 1) Limit up to 1
Ashish
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