A Systematic Approach for Developing a Numerical Wavetank to Simulate Driven Shallow- and Deep-Water Waves

Numerical models of wavetanks for nonlinear waves driven by waveflap/piston wavemakers are developed. Variational principles (VPs) for the underlying equations of nonlinear potential-flow dynamics are implemented directly in the finite-element-based environment Firedrake. The establishment of mathematical and numerical wavetank models, based on VPs and domain-specific compiler architecture, is a novel challenge aimed at both reducing time-to-development and enabling new model experimentation. The waveflap-wavemaker problem is fundamentally more complex than the piston-wavemaker problem since reformulation of the mathematical problem into a computational domain respectively demands multi- and single-step transformations because of the respective two- and one-dimensional wavemaker motions. Hence this paper presents a systematic approach for developing a numerical piston/waveflap wavemaker wavetank, within the widely available Firedrake environment, that can simulate the dynamics of both shallow- and deep-water waves.