In the wave tank whose picture is attached, a flap-type wavemaker is turned on at time t = 0 and waves are generated which propagate down the channel. If the frequency and throw of the wavemaker are adjusted appropriately, the waves generated are in the formal range of validity of various model equations. Namely, initial-boundary-value problems.
Naturally, one needs to understand whether or not the relevant problems have solutions. The solutions should also vary only slightly with small variations of the imposed boundary conditions - i.e. the model should be robust. The relevant model equations are nonlinear and exact solutions are not available even for very simple boundary data. Thus, when such models are used in practice, a numerical scheme for approximating its solutions must be implemented. Will this have an unwanted, artificial effect on the solutions? Theory relating to this will be discussed.