Numerical Simulation of Free Vortex Flows by Level Set Method

摘要

This paper uses a level set function to capture the interface between air and water. The three-dimensional incompressible Navier-Stokes equations are used to solve the gas-liquid two phase flow system. In order to maintain the level set function as a smooth signed distance function from the interface, a reinitialization operation is required. We also apply a constraint to improve the conservation of mass significantly. A WENO scheme for space derivatives and third-order Runge-Kutta scheme for the time discretization are used to solve the level set equation. The projection method are used to derive a pressure Poisson equation to ensure the satisfaction of continuity equation. The velocity field can be obtained by second-order explicit Adams-Bashforth scheme, while the pressure is solved. The model allows us to simulate a wide range of flow regimes and surface tension effect can be consideration. We use the Zalesak's problem to test the accuracy of the model. This study applied to simulate three-dimensional free vortex flow problem. By adding if or not artificial perturbation to observe producing the vortex in different cases.