Author(s)

José Marie Orellana

Mathematical and Numerical Modelling Laboratory (M2N), National Conservatory of Arts and Crafts, Paris, France.

The objective of this paper is to present a new method for designing absorbing or non-reflective boundary conditions (ABC) or (NRBC), illustrated by the case study of the modelling of a solid body in water, specifically the capillary gravity waves generated by its motion at the surface. The study analyses the flow of an inviscid, barotropic, and compressible fluid around the stationary solid body. The dynamic behaviour of the fluid is analysed using a two-dimensional coupled Neumann-Kelvin model extended with capillarity and inertia terms. For computational purposes, it is necessary to truncate the unbounded spatial domain with artificial boundaries and then introduce appropriate absorbing boundary conditions. The propagation of short wavelength waves in a convective fluid medium with significant differences in properties between the interior and the surface of the fluid presents a number of difficulties in the design of these conditions. The results are illustrated numerically and commented upon.

Absorbing Boundary Condition, Fluid-Structure Interaction, Capillary-Gravity Waves, Numerical Simulations

Orellana, J. (2024) Absorbing Boundary Conditions for Simulating Water Waves Near Solid Bodies. Journal of Applied Mathematics and Physics, 12, 3502-3520. doi: 10.4236/jamp.2024.1210208.