[jd87]

It is a peculiar thing I noticed that the 1st order FDM scheme gives a realistic result than a 2nd order one-sided FDM scheme for approximating first-order derivatives. See the image below for the one-sided approximation.

[IMG]https://doc-0c-2s-docs.googleusercontent.com/docs/securesc/ha0ro937gcuc7l7deffksulhg5h7mbp1/jtrqejfqmdige42m1bjdhnpue7r3o5t9/1553076000000/02266267703806582586/*/1WrAE_vC_RLNlIgQPHusJ2AOmB2HPjG3A[/IMG]

I am using a one-sided approximation for a simple 2nd order upwind scheme wherein my velocity is positive at i=3 (I want to avoid a 1st order scheme for numerical diffusivity issues). Now, because of this anomaly, my code is predicting a negative concentration in spite of concentration at the boundary is 1 (u1) and all other points are zero (u2, u3 and so on) at the initial time. Please note, I have written a 3D geometric multigrid code but given the example of a 1D situation for easier explanation. Since in the first time I am encountering a negative u, the later times are therefore giving all wrong results. It would be really kind of any of the members to let me know is there any simpler scheme to get rid of this issue without sacrificing the 2nd-order accuracy. Thank you in advance.