a reduced model for internal waves interacting with submarine ...

The AM4 scheme used is:
η n+1
j
V n+1
j
=η n j + ∆t ( 251E
n+1
j + 646E n j
720
− 264En−1 j + 106E n−2
j
= V n j+ ∆t ( 251F
n+1
j + 646F n j
720
− 264Fn−1 j + 106F n−2
j
− 19E n−3 )
j ,
− 19F n−3 )
j .
To initialize both predictor-corrector schemes, the RK4 described above is
employed.
4.3 Flat bottom experiments
Example 4.1. We first consider the LFM for the non dispersive caseβ=0,
⎧
⎪⎨ η t = u 1ξ ,
⎪⎩ u 1t =η ξ .
(4.8)
This is just the bidirectional wave equation forη
η tt −η ξξ = 0
with initial contidions
η(ξ, 0)=η 0 (ξ),
⎧⎪⎨⎪⎩
η t (ξ, 0)=u 10ξ (ξ).
This model (whose exact solution is well known) is useful for validating and comparing
the numerical schemes, since it is more demanding than the dispersive
models regarding numerical stability, as we commented in the previous Section.
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