About Eq. (1.26) in section "Implicit methods"

[astroboylrx]

I believe that Eq. (1.26) at here does not want expansions on time. I think the superscript of "t" on the right hand side should be changed from "n" to "n+1".
PS: I think the subscript of the Jacobin matrix, "0", may be a little confusing since the matrix uses digits (1-n) as the subscriptions of its elements. Maybe a few more explanations will make it clearer. Thanks.

[zingale]

you are right -- that's a typo (the n instead of n+1). The proper superscript appears in 1.28.

I'll think about the notation issue as well.

[astroboylrx]

I found another two typos:

• Eq. (3.11) : I think the right-hand-side should be 1+C^2 \sin^2\theta
• Exercise 4.1 : to solver => to solve

Extend your 1-d finite-volume solver for advection to solver Burgers' equation.

Sorry for my trivial comments on small things. :-)

[astroboylrx]

Maybe another typo in Exercise 3.10 at here:

However: you may find less than second-order is your initial conditions have discontinuities and you are limiting.

Maybe the original meaning is "you may find less second-order since your initial conditions have discontinuities and you are limiting"?
Thanks.

[astroboylrx]

About Figure 3.13 (tex code here):
I couldn't reproduce it with minmod limiting method (the results are less than second order as described in Exercise 3.10). Later on, I found it was done by "centered" slope_type in your code, which means unlimited. I think the caption of Figure 3.13 is kind of misleading.

Thanks!

[zingale]

yes, you are right about FIgure 3.13. I've explicitly added several different limiters to that plot now.

[astroboylrx]

Seems another typo in Eq. (3.58):
I think the sign between the two fractions inside the square brackets should be plus:

a_{i,j}^{n+1} = a_{i,j}^n - \Delta t \left [
   \frac{(ua)_{i+\myhalf,j}^{n+\myhalf} - (ua)_{i-\myhalf,j}^{n+\myhalf}}{\Delta x} +
   \frac{(va)_{i,j+\myhalf}^{n+\myhalf} - (va)_{i,j-\myhalf}^{n+\myhalf}}{\Delta y} \right ]

Thank you! :-)

[zingale]

yes, you are correct