A generalized variational level set method without frequent reinitialization for simulations of gas-liquid flows

A generalized variational level set method without frequent reinitialization process is proposed to address the issue of the traditional level set method for detailed numerical simulations of gas-liquid flows. The gas-liquid interface is captured by the level set method and the discontinuity across the interface is discretized by the ghost fluid method. A penalty term is added in the classical level set advection equation to reduce the frequent reinitialization process. The effect of the frequency of the reinitialization step on the performance of the level set method is evaluated and the effect of the penalty factor on the interface evolution is investigated in the present work. Three typical benchmark cases, including rigid body rotation, two-dimensional shear motion, and three-dimensional shear motion, are used to validate the accuracy of the present variational level set method. It is found that the reinitialization process is not necessary for every time step with the penalty term. A spatially averaged parameter near the interface is proposed to quantitatively evaluate the necessity of reinitialization. The present method is also shown to have second-order accuracy. This work provides an accurate and efficient way to simulate the gas-liquid flows.