Talk:Finite volume method

Looks to me like there is a sign error in equations (4), (5), and (6). Someone should verify, but it appears that when df/dx was moved to the right hand side, it was not turned negative.

Think about it, for the amount of rho at time two to be greater than at time one, you need a net decreasing flux to the right (df/dx must be negative). Thus for the integral in equation (4) to be valid, it must be subtracted from the initial amount of rho.

The same correction is needed with (5), and with (6) either the sign on the flux integrals should be swapped, or the indexes can be. When the equation was re-arranged in (7), correct sign convention appears to be in order again.

If this is the case and I'm not just going nuts about nothing, someone with equation-editing know-how ought to give it a quick adjust. --LANMasta (talk) 23:41, 10 August 2009 (UTC)Reply

• You are correct and I have made the necessary changes. I have also made some other minor modifications that I hope will aid understanding. Griffgruff (talk) 10:13, 15 August 2009 (UTC)Reply

I would modify the subject "General hyperbolic problem" into "General conservation law". In fact, the form of equation there reported is the general form of a conservation law, which need not be always hyperbolic. For instance, Navier-Stokes equation without external forcing term have that same general form, but they're parabolic instead of hyperbolic. Waiting for agreement by previous authors. Giorgio.bornia (talk) 15:45, 12 November 2009 (UTC)Reply

• Good point - done! Griffgruff (talk) 11:31, 23 January 2010 (UTC)Reply

To me the proof seems wrong from equation (6) to equation (7). While the proof describes that (7) is obtained from (6) by differentiating (6) with respect to time, what is needed instead is

1. Divide the equation by Δt,

2. Assume t_2 = t_1 + Δt,

3. Let Δt -> 0, and assume t_1 is a general time t.

Can someone confirm this? Schimmel-chip (talk) 08:53, 12 April 2024 (UTC)Reply