Hi, I know the general form of the Navier Stokes Equation as follows. I am following a software paper of "Gerris flow solver written by Prof. S.Popinet" [Link:http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.374.5979&rep=rep1&type=pdf] and he mentions after time discretization he ends with the following equation: where n-1 is the previous time step, n+1 is the next time step and n+0.5 is mid time for the present time step. Solving equation implicitly/ explicitly in time means solving for next time data however in the equation there are rather two unknowns un+0.5 and un+1. Not sure why he uses different terms at different time intervals. Density at n+0.5, velocity at n, n-1, n+0.5 etc.. Can anyone point me or explain me how he arrives at this specific sort of discretized equation.