A generating and absorbing boundary condition for dispersive waves in detailed simulations of free-surface flow interaction with marine structures

Abstract

The boundaries of numerical domains for free-surface wave simulations with marine structures generate spurious wave reflection if no special measures are taken to prevent it. The common way to prevent reflection is to use dissipation zones at the cost of increased computational effort. On many occasions, the size of the dissipation area is considerably larger than the area of interest where wave interaction with the structure takes place. Our objective is to derive a local absorbing boundary condition that has equal performance to a dissipation zone with lower computational cost. The boundary condition is designed for irregular free-surface wave simulations in numerical methods that resolve the vertical dimension with multiple cells. It is for a range of phase velocities, meaning that the reflection coefficient per wave component is lower than a chosen value, say 2%, over a range of values for the dimensionless wave number kh. This is accomplished by extending the Sommerfeld boundary condition with an approximation of the linear dispersion relation in terms of kh, in combination with vertical derivatives of the solution variables. For this article, the boundary condition is extended with a non-zero right-hand side in order to prevent wave reflection, while, at the same time, at the same boundary, generating waves that propagate into the domain. Results of irregular wave simulations are shown to correspond to the analytical reflection coefficient for a range of wave numbers, and to have similar performance to a dissipation zone at a lower cost.