A Conservative Level Set method for interface capturing in two-phase flows

This paper presents a novel conservative Level Set (LS) method for inter- face capturing in two-phase flows. The purpose of this study is to compare the method with Volume of Fluid (VOF) and analytical or experimental results. Second order Finite Volume (FV) method is used for domain discretization. The most common approach for interface capturing with FV is the VOF method which is conservative. Special treatment in discretization is required to maintain a sharp inter- face, which can cause numerical difficulties. The LS method ([2], [3]) is based on a signed distance function to keep track of the interface and avoids this problem. However, a draw- back of the LS method is lack of mass conservation since the signed distance function does not represent any preservable physical quantity. This paper describes a novel approach to conserve the volume using the LS method for incompressible two-phase flows. After the advection of the LS variable, global volume change is measured and the signed distance function is explicitly corrected via source term to compensate for volume change. The value of the term is iteratively obtained by successive linear approximations to a given tolerance. To correct the signed distance function, a redistancing equation is used, as presented in [4]. The redistancing equation is reformulated to allow solving it implicitly. The complete mathematical model is implemented in the open source CFD software Open- FOAM [5]. It is based on incompressible Navier-Stokes equations with Newtonian viscos- ity. The pressure-velocity coupling is solved using the PISO algorithm. Validation of the implemented method is done on two test cases. The first case describes a standing wave in a 2D wave tank. The second case describes a 3D dam break on a square column [7].