Stabilized finite element methods for solving the level set equation without reinitialization

New stabilized finite element methods are proposed for solving moving interface flow problems using the level set approach. The formulations enhance the interface resolution without the need to resort to the reinitialization process. These are established by adding a perturbation term that depends on the local residual of the Eikonal equation to the SUPG variational formulation of the level set equation. These methods are numerically evaluated for well-known benchmark flow problems and compared with a modified variant of the penalty method of Li et al. (2005). The proposed stabilized finite element methods employing second-order time and space approximations are promising simple and accurate techniques for solving complex moving interface flows.