An unsteady single‐phase level set method for viscous free surface flows

Abstract

Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. ABSTRACTThe single-phase level set method for unsteady viscous free surface flows is presented. In contrast to the standard level set method for incompressible flows, the single-phase level set method is concerned with the solution of the flow field in the water (or the denser) phase only. Some of the advantages of such an approach are that the interface remains sharp, the computation is performed within a fluid with uniform properties and that only minor computations are needed in the air. The location of the interface is determined using a signed distance function, and appropriate interpolations at the fluid/fluid interface are used to enforce the jump conditions. A reinitialization procedure has been developed for non-orthogonal grids with large aspect ratios. A convective extension is used to obtain the velocities at previous time-steps for the grid points in air, which allows a good estimation of the total derivatives. In this report we discuss the details of such implementations. The method was applied to three unsteady tests: a plane progressive wave, sloshing in a two-dimensional tank, and the wave diffraction problem in a surface ship, and the results compared against analytical solutions or experimental data. The method can in principle be applied to any problem in which the standard level-set method works, as long as the stress on the second phase can be specified (or neglected) and no bubbles appear in the flow during the computation.

Front tracking with moving-least-squares surfaces

“…The aforementioned drawbacks of Lagrangian methods have made Eulerian methods, such as the Volumeof-Fluid (VOF) method [20,32] or the Level-Set (LS) method [30,33,37,27,29,34] (or combinations thereof [36,39]) to be preferred in the modeling of complex interfaces undergoing topological changes such as bubble coalescence, wave breaking, etc [40,38,47,8,9]. Eulerian methods are based on the advection of a scalar field φ defined on the whole flow domain.…”

Computation and Experiment of Propeller Thrust Fluctuation in Waves for Propeller Open Water Condition

“…Only the water side of the flow field is computed and for satisfying the kinematic and dynamic free surface boundary conditions, jump conditions are imposed at the free surface. These conditions result in equations for extension velocities in the air side, and in pressure interpolations to satisfy atmospheric pressure at the free surface 21) . For discretization of time, convective and viscous terms second-order finite difference methods are utilized.…”

Isogeometric boundary-element analysis for the wave-resistance problem using T-splines

“…During the last 50 years, the interest in numerical methods for calculating ship wave resistance has been constantly growing. Computations are performed using a variety of techniques, ranging from the simple Michell's thin-ship theory [5] to extremely complex and costly methods such as the fully non-linear Reynolds Averaged Navier Stokes Equations (RANSE) [6,7,8]; see the reports by the International Towing Tank Conference ( [9,10,11]) and the references cited therein.…”