Modified Lagrangian vortex method with improved boundary conditions for water waves past a thin bottom-standing barrier

Abstract

Herein, the modified Lagrangian vortex method (LVM), a hybrid analytical-numerical algorithm per se, is devised to simulate the process of vortex formation and shedding from the sharp edge of a zero-thickness vertical plate under linear water-wave attack. Application of the Helmholtz decomposition facilitates a convenient switch between the inviscid- and viscous-flow models, thereby enabling easy incorporation of vorticity effects into the potential-flow calculations for the viscous-dominated region. In evaluating the potential-flow component, making good use of the quickly convergent technique with singular basis functions, correctly capturing the singular behavior in velocity fields near the tip of the plate, leads to a considerable reduction of computational burdens and to 12-decimal-place accuracy. The viscous correction is carried out via the meshless LVM with improved boundary conditions. Comparisons with previously published results show good agreement. Simulations of vortex generation and evolution illuminate the ability of the present method, and provide a supplement to pertinent experimental works. The hybrid scheme proposed herein allows flexibility for the former LVM and convenience in the code development. Such a compromise fits particularly well for the high-resolution modeling of sharp-edged vortex shedding without heavy numerical developments. © 2014 John Wiley & Sons, Ltd.