I try to apply modified PDE approach to first-order upwind scheme while I am reading the fluid simulation book1 by Robert Bridson today.

The procedure is very similar to which I used in my previous post. However the viscosity term I get is a bit different from the ones in the book.

This is my code:

The result I get is:

The modified PDE(up to a second-order truncation error) I get is

which is different from the one in the book:

## References

1. Bridson, Robert. Fluid simulation for computer graphics. CRC Press, 2015.