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$\begingroup$ Thanks for your answer. As you suggested, I tried to implement a CTCS scheme (with Dirichlet BC and a simple 2D gaussian as initial condition) but the result still unstable though... Leveque's text is very complete about how discritizing 1D advection equations with constant veocity transport but how about generalization in higher dimensions and with space dependant velocity flow $\textbf{v}$? It seems to me that a given stable 1D scheme can lead to an unstable one when directly transposed in 2D (I found an interesting work dealing this issue). $\endgroup$
– dolun
Commented Oct 20, 2014 at 15:06
$\begingroup$ Since you have a new question, you should post it! But not in the comments, please. $\endgroup$
– David Ketcheson
Commented Oct 20, 2014 at 16:13

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