Generating–absorbing sponge layers for phase-resolving wave models

• We develop absorbing-generating sponge layers for phase-resolving wave models.
• Solutions for free waves are imposed in sponge layers to generate waves.
• Solutions may be made arbitrarily accurate through choice of coefficients.
• The methodology works well for linear, nonlinear, and irregular waves.

The accurate generation and absorption of water waves in phase-resolving models are critical issues in representing nearshore processes. Here, we present a source function method for combined wave generation and absorption using modified sponge layers. This technique can be easily adapted to a wide variety of systems, and does not require the solution of Green's functions but rather the simpler knowledge of solutions for free waves. These solutions may be linear or nonlinear, regular or irregular, and generated waves can be made arbitrarily accurate through simple selection of sponge layer coefficients. Generating–absorbing sponge layer systems are shown to have a close correspondence to relaxation zones for wave generation if relaxation coefficients are chosen appropriately.