An efficient model for three-dimensional surface wave simulations. Part II: Generation and absorption

Water wave generation procedures and efficient numerical beaches are crucial components of a fully non-linear numerical tank for water wave simulations. Linear formulae for pneumatic wave makers are optimized for efficient fully non-linear wave generation in three dimensions. Analytical integration of the (linear) applied free surface pressure provides formulae valid for all times of the simulation. The purely non-linear part of the wave making procedure becomes integrated in the fully non-linear formulation. Novel numerical beaches are introduced, damping the (scaled) tangential velocity at the free surface. More specifically, an additional term is introduced in the Bernoulli equation at the free surface, namely ∇-1·(γ∇ϕ˜), where γ is a non-zero (smooth) function in regions where damping is required and zero in the wave propagation domain, ∇ϕ˜ is the scaled tangential velocity at the free surface, and ∇−1 the inverse horizontal gradient operator. The new term results in a modified dynamic free surface condition which is integrated in time in the fully non-linear formulation. Extensive numerical tests show that the energy of the outgoing waves is completely absorbed by the new damper. Neither wave reflection nor emission are observed. A steep solitary wave is completely absorbed at the numerical beach. Damping of waves due to advancing pressure distributions are efficient as well. The implementation of the absorber in any existing numerical tank is rather trivial.