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this is actually quite easy. We can get rid of the PLM routines and instead define and I(nu) as
I(nu) = q_i + 1/2 (1 - dt/dx lambda(nu) ) dq_i
for the left state (and an analogous one for the right state), and then just use this in the PPM tracing routines instead of the integrals under the parabola.
Then, we define the reference state as it is currently done with PLM, e.g., for the left state,
The basic structure of the characteristic tracing is the same for PLM and PPM, but we have separate tracing routines. We should merge these together.
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