A least-square weighted residual method for level set formulation

In this paper, a least-square weighted residual method (LSWRM) for level set (LS) formulation is introduced to achieve interface capturing in two-dimensional (2D) and three-dimensional (3D) problems. An LSWRM was adopted for two semi-discretized advection and reinitialization equations of the LS formulation. The present LSWRM provided good mathematical properties such as natural numerical diffusion and the symmetry of the resulting algebraic systems for the advection and reinitialization equations. The proposed method was validated by solving some 2D and 3D benchmark problems such as those involving a rotating slotted disk, the rotation of a slotted sphere, and a time-reversed single-vortex flow and a deformation problem of a spherical fluid. The numerical results were compared with those obtained from essentially non-oscillatory type formulations and particle LS methods. Further, the proposed LSWRM for the LS formulation was coupled with a splitting finite element method code to solve the incompressible Navier-Stokes equations, and then, the collapse of a 3D broken dam flow was well simulated; in the simulation, the entrapping of air and the splashing of the surge front of water were reproduced. The mass conservation of the present method was found to be satisfactory during the entire simulation.