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6.1 Splitting advection from the rest

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Start by splitting the entire evolution into a sequence of alternating advection and non-advection phases

\frac{\partial f}{\partial t}+\frac{\part...
...l t} = G(f)}
\qquad &\textrm{(all the rest)}
\end{array}\right.\end{displaymath}     (1)

The advection part (including the convective derivative) is first evolved by propagating the solution along the characteristics; this is achieved using a Lagrangian method such as the explicit cubic-interpolated propagation (CIP) scheme, which is explicit and has no restriction on the time step. After this interpolation from the characteristics back to Eulerian coordinates, the second non-advection part can then be solved using one of the methods that have been discussed previously.

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