An adaptive numerical scheme for solving incompressible 2‐phase and free‐surface flows. (26th March 2018)

• Record Type: Journal Article
• Authors: Frey, P.; Kazerani, D.; Ta, T.T.M.
• Is Part Of: International journal for numerical methods in fluids. Volume 87:Number 11(2018)
• Page Start: 543
• Page End: 582
• Publication Date: 2018-03-26
• Subjects: anisotropic mesh adaptation -- finite element method -- free‐surface flows -- incompressible Navier‐Stokes equations -- level‐set method -- method of characteristics -- 2‐phase flows; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4502
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: In this paper, we present a numerical scheme for solving 2‐phase or free‐surface flows. Here, the interface/free surface is modeled using the level‐set formulation, and the underlying mesh is adapted at each iteration of the flow solver. This adaptation allows us to obtain a precise approximation for the interface/free‐surface location. In addition, it enables us to solve the time‐discretized fluid equation only in the fluid domain in the case of free‐surface problems. Fluids here are considered incompressible. Therefore, their motion is described by the incompressible Navier‐Stokes equation, which is temporally discretized using the method of characteristics and is solved at each time iteration by a first‐order Lagrange‐Galerkin method. The level‐set function representing the interface/free surface satisfies an advection equation that is also solved using the method of characteristics. The algorithm is completed by some intermediate steps like the construction of a convenient initial level‐set function (redistancing) as well as the construction of a convenient flow for the level‐set advection equation. Numerical results are presented for both bifluid and free‐surface problems. Abstract : We present a numerical scheme for solving incompressible two‐phase and free‐surface flows. Our method is based on anisotropic mesh adaptation and on level‐set method. Different numerical tools and the global algorithm are described. Finally, some numerical results are illustrated.