A Novel Least-Squares Level Set Method by Using Polygonal Elements

In this study, we apply an artificial viscosity method to convert unsteady level set (LS) convection equation into LS convection-diffusion transport stabilize the numerical solution of term. Then a novel least-square polygonal finite element is used solve problem. The least-squares provided good mathematical properties such as natural diffusion and positive definite symmetry resulting algebraic systems for re-initialization equations. proposed evaluated numerically in two different benchmark problems: rigid body rotation Zalesak’s disk, time-reversed single-vortex flow. comparison with conventional triangular (T3) quadrilateral (Q4) elements, elements are capable providing greater flexibility mesh generation complicated problems well more accurate solving addition, results also compared which obtained from essentially non-oscillatory type formulations particle methods. show that completely matches previously published results.