Shallow Water Equation

I have been looking into the shallow water equation but there is an issue with my simulation. Particles aren’t propagating correctly think I’m misunderstanding the equations.

My question is assuming you have an array of h,vx,vy how do you write the equation for f1 and f2? I’m kinda confused by the term

eiuiuj, I’m currently writing that for diagonals as 2*(dx/dt)(dx/dt)(vx+vy) for f2 and cardinal using f1 as an example, (dx/dt)(dx/dt)vxvx.
I am taking ei
uiuj to be equivalent to (eiui)^2 which I have seen in other papers. Some pseudo code or some code to look at would be much appreciated.

Hi ChaseRLewis,
did you make any progress in simulating free flows? I’ll be interested in learning more.
Also, did you check other papers as well on the topic for LBM?