A hybrid finite-boundary element method for inviscid flows with free surface

Abstract Different formulations of free-surface inviscid flows lead to Fredholm integral equations of the first or second kind. In the present study, these formulations are compared in terms of efficiency and accuracy when different time and space discretization schemes are employed in studying inviscid oscillations of a liquid drop. A hybrid scheme results from combining a boundary integral equation approach for the Laplacian with a Galerkin/finite-element technique for the kinematic and dynamic boundary conditions. It is found that the fourth-order Runge-Kutta method is the most efficient among various schemes tested for integration in time and that cubic splines should be preferred as basis functions over conventional Lagrangian basis functions. Furthermore, the formulation based on the integral equation of the second kind is found to be more prone to short-wave instabilities. However, if numerical filtering is applied in conjunction with it, then the time-step used can be twice as large as that required by the unfiltered integral equation of the first kind. Results compare well with analytic solutions in the form of asymptotic expansions.