On the reinitialization procedure in a narrow-band locally refined level set method for interfacial flows

Abstract

SUMMARYA local level set algorithm for simulating interfacial flows described by the two-dimensional incompressible Navier-Stokes equations is presented. The governing equations are solved using a finitedifference discretization on a Cartesian grid and a second-order approximate projection method. The level set transport and reinitialization equations are solved in a narrow band around the interface using an adaptive refined grid, which is reconstructed every time step and refined using a simple uniform cell-splitting operation within the band. Instabilities at the border of the narrow band are avoided by smoothing the level set function in the outer part of the band. The influence of different PDE-based reinitialization strategies on the accuracy of the results is investigated. The ability of the proposed method to accurately compute interfacial flows is discussed using different tests, namely the advection of a circle of fluid in two different time-reversed vortex flows, the advection of Zalesak's rotating disk, the propagation of small-amplitude gravity and capillary waves at the interface between two superposed viscous fluids in deep water, and a classical test of Rayleigh-Taylor instability with and without surface tension effects. The interface location error and area loss for some of the results obtained are compared with those of a recent particle level set method.

On Simulating Primary Atomization Using the Refined Level Set Grid Method

“…Details on the method when used in conjunction with a structured, equidistant Cartesian flow solver grid and its performance in generic advection test cases can be found in [6,16]. To a certain extent the RLSG method is similar to the recently proposed Narrow-Band Locally Refined Level Set (NBLR-LS) approach [17]. However, the latter is limited to Cartesian grids, whereas the former can deal with arbitrary unstructured flow solver meshes.…”

“…Here we will use a slight modification to the criterion proposed by Gomez et al [17]. The PDEbased re-initialization procedure is applied only if max(|∇G|) > α max or min(|∇G|) < α min , (10) evaluated inside the transport band T -band (see [6,16] for definition of the individual bands).…”

“…This is a common test problem analyzed by a variety of different methods [17,29,30,31]. A heavy fluid, ρ 1 = 1.225, µ 1 = 0.00313, is placed above a light fluid, ρ 2 = 0.1694, µ 2 = 0.00313, inside a domain of size 1x4.…”

Trends in Comprehensive Modeling of Spray Formation

“…In such approach the level-set equations are solved on a refined grid that is finer than the solution for the flow. The grid can be made finer in the vicinity of the interface (as shown in [25]). Also, the use of a much finer Cartesian grid can be used for the level-set equation with an unstructured grid for the flow solution [24].…”

CFD Analysis in Subsea and Marine Technology

“…Furthermore, the discretisation error in the transport appears as a loss of unit gradient for the distance function; as a result, the advection step is usually followed by re-initialisation. This can be done by direct calculation of distance [16] in a narrow band, or by solving an additional Eikonal equation to propagate the unit gradient constraint [17]. The best methods use implicit re-initialisation [12] or combine mass conservation properties of VOF and smoothness of LS in some way [11]; • Phase Field (PF) methods are developed on a basis that there exists a transport equation for self-similar advection of a tanh profile [18].…”