A multi-level adaptive mesh refinement method for level set simulations of multiphase flow on unstructured meshes

An adaptive mesh refinement (AMR) technique is proposed for level set simulations of incompressible multiphase flows. The present AMR technique is implemented for two-dimensional/three-dimensional unstructured meshes and extended to multi-level refinement. Smooth variation of the element size is guaranteed near the interface region with the use of multi-level refinement. A Courant–Friedrich–Lewy condition for zone adaption frequency is newly introduced to obtain a mass-conservative solution of incompressible multiphase flows. Finite elements around the interface are dynamically refined using the classical element subdivision method. Accordingly, finite element method is employed to solve the problems governed by the incompressible Navier–Stokes equations, using the level set method for dynamically updated meshes. The accuracy of the adaptive solutions is found to be comparable with that of non-adaptive solutions only if a similar mesh resolution near the interface is provided. Because of the substantial reduction in the total number of nodes, the adaptive simulations with two-level refinement used to solve the incompressible Navier–Stokes equations with a free surface are about four times faster than the non-adaptive ones. Further, the overhead of the present AMR procedure is found to be very small, as compared with the total CPU time for an adaptive simulation.