On comparison of the sharp-interface and diffuse-interface level set methods for 2D capillary or/and gravity induced flows

The present work is on comparison of numerical-methodology as well as performance of the two types of level set methods (LSMs): sharp-interface and diffused-interface. The numerical-methodology along with mathematical-formulation are presented in-detail for relatively recent ghost fluid method based sharp-interface level-set-method (SI-LSM); and compared with the methodology for the traditional diffuse-interface level-set-method (DI-LSM) as well as an improved diffuse-interface dual-grid-level-set-method (DI-DGLSM). Two different types of surface models are considered: continuum surface force (CSF) and sharp surface force (SSF) model; CSF model for the DI-LSM and SSF model for the SI-LSM. The SI-LSM considers the physically realistic sudden variation of the thermo-physical property across the sharp-interface while DI-LSM considers a smoothened value of the properties across the numerically diffused-interface. For solving the pressure Poisson equation in the SI-LSM, a finite volume method based generic formulation is proposed and its implementation-details are presented. For the SI-LSM as compared to DI-LSM and DI-DGLSM, the relative performance study is presented on four reasonably different two-phase problems: surface-tension model induced unphysical flow for a static water droplet, collapse of a water-column in air, falling of a water-droplet in air, and coalescence of an ethanol-droplet over a pool of ethanol in air. For the performance study on various problems, a comparison of the results obtained by the three types of LSMs (SI-LSM, DI-LSM and DI-DGLSM) and various other numerical methods in the literature are presented. SI-LSM as compared to DI-LSM and DI-DGLSM is shown to substantially reduce the unphysical spurious velocity and results in better accuracy on the same grid size.