Finite Differencing with Incompressible Navier Stokes Equations (Only Advection)
 

Hi,

I'm trying to improve the advection method in a CFD Simulation of a 2D-windfield. The Navier Stokes Equations are currently used for the influence of pressure, viscosity,... I am just focusing on the convective acceleration term.
Now I have an equation for the velocity u in x-direction and v in y-direction.Attachment 97340
My question is, can I now just apply for example backward differerencing so that I get the two final equations: Attachment 97341.

Its not working properly in the simulation for example if the direction of the wind should change over time, the direction stays the same but the velocity on the edges of the field (where the initial conditions of u and v are set) are getting bigger or smaller, depending on the "direction of the change". It seems like the information is not spreading properly over the whole wind field.

I'm new to CFD, so please be gentle with me.
Thank you for any advice.