A multi-level adaptive mesh refinement for an integrated finite element/level set formulation to simulate multiphase flows with surface tension

Abstract

A multi-level adaptive mesh refinement technique for an integrated finite element/level set formulation was implemented to simulate the incompressible interfacial flows with surface tension by using unstructured P2P1 triangular and tetrahedral meshes. Linear/quadratic elements near the interface were dynamically refined as an interface evolves in order to produce an accurate solution with a lower computational cost. An adaptive mesh refinement algorithm for a linear element has been extended to a quadratic element by using a node-reordering. The proposed algorithm was successfully validated by solving several benchmark problems. Simulation of a static bubble problem was found to give an accurate solution with negligible spurious currents compared with existing results. Simulation results of rising bubble problems in 2D and 3D were also compared against existing numerical and experimental results in terms of terminal rising speed and terminal bubble shape. We have found that the present algorithm provided stable and accurate solutions even for a high density-ratio and that the solution accuracy strongly depended on the mesh resolution near the interface. Further, the present algorithm was shown to be very efficient because the computational overhead by mesh-refinement algorithm was very small compared to the elapsed times consumed for solving the incompressible Navier–Stokes equations and the advection/re-initialization equations of level set method. Lastly, the coalescence scenario of two oblique bubbles was well reproduced by the present 3D simulation.