Finite elements using a plane-wave basis for scattering of surface water waves

Area of Science:

• Fluid dynamics
• Computational physics
• Numerical analysis

Background:

• Accurate simulation of water waves is crucial for coastal engineering and oceanography.
• Existing numerical methods often struggle with combined wave phenomena or high frequencies.
• Frequency-independent methods are desirable for broader applicability.

Purpose of the Study:

• To propose a generalized, frequency-independent finite-element method (FEM) for simulating complex water wave interactions.
• To extend existing numerical integration techniques for enhanced efficiency in wave simulations.
• To provide a robust numerical tool for analyzing combined diffraction, refraction, radiation, reflection, and absorption of water waves.

Main Methods:

• A generalized, frequency-independent finite-element method (FEM) is developed.
• Plane waves are utilized as an external function space within the FEM framework.
• An existing integration method for wave diffraction is extended to handle combined refraction and diffraction.
• Boundary conditions are imposed efficiently by applying the FEM to plane waves on each element.

Main Results:

• The proposed FEM successfully simulates combined diffraction, refraction, radiation, reflection, and absorption of water waves.
• The method demonstrates significant computational savings in operations for a given error compared to standard numerical integration.
• The extension of the integration method proves effective for high-frequency wave scenarios.

Conclusions:

• The generalized, frequency-independent FEM provides an efficient and accurate numerical simulation tool for various water wave phenomena.
• This method offers substantial computational advantages, particularly for high-frequency wave problems.
• The approach enhances the capability for analyzing complex wave interactions in fluid dynamics.