Originally Posted by siamak 60 (Post 691086)

hi
I want to write code with matlab using dufort frankel method.
two equation exist for this work . momentum equation in x direction for obtaining velocity inside boundary layer. consider gradient of pressure gradient at x direction as zero but in y direction is not zero.
continuity equation for determining velocity inside boundary layer at y direction.
what should i do for finding unknown variable. should i first determine all velocity in x direction by an approximate method like pohlhousen ? if i do that; then i shall believe that some finite difference method like dufort frankel is useless unless it will be used to optimize results obtained by an approximate method ?
Thanks for your time

Originally Posted by siamak 60 (Post 691107)

Laminar Boundary Layer
Momentum in X-Direction (steady state, Incompressible flow):
u ∂u/∂x+V ∂u/∂y=v (∂^2 u)/〖∂y〗^2
Dufort-Frankel finite Difference Discretization:
u(i,j)*((u(i+1,j)-u(i-1,j))/(2*∆x)+V(i,j)*((u(i,j+1)-u(i,j-1)))/(2*∆y)=v ((u(i,j+1)-2*u(i,j)+u(i,j-1))/〖∆y〗^2
Above finite difference form of momentum equation shall be used to find all u(i,j) inside boundary layer.
Continuity equation:
∂u/∂x+∂V/∂y=0
Dufort-Frankel form
(u(i+1,j)-u(i-1,j))/(2*∆x)+(V(i,j+1)-V(i,j-1))/(2*∆y)=0
Above finite Difference form of continuity equation shall be used to drive V(i,j) .

For using these equations it seems that you shall have all values of u(i,j) and Dufort-Frankel will only optimize these values. These initial values of u(i,j) can be driven from approximated methods like Karman-Pohlhausen:
u/U_∞ =2*y/δ-〖(y/δ)〗^2
δ/x=√(30/((xU_∞)/v))
My questions are :1) isn’t any direct method to use Dufort-Frankel Method ?
2) Is described method a correct method for using Dufort- Frankel ?