Hello:

I am doing my research in proppant transport in pkn type fracture networks. I have modeled the fractures with 3D cohesive elements in Abaqus, and I have labelled certain nodes to be the injection points for the proppants and fluid (aka., slurry) to flow into the fracture through these injection nodes. Proppants, being basically sand particles, cannot travel towards the top of the fracture because of gravity. Also, the pressure of the whole system is higher at the inlet than anywhere else, there is no backflow of proppants back to the inlet either.

Therefore, after discretizing the fracture in x and z directions, at any point, proppants can only come from the left side of the x-direction and settle down towards the bottom which is downwards of the z-direction. This is demonstrated in the image file "Image 1.png".

Is it possible that in x-direction, I use the upwind method and in z-direction, I use the downwind method? In the word document titled "equation.docx", I have written down the discretized form of the 2D advection equation.

Thank you very much!

Mousumi