Finite Difference and Reinitialization Methods with Level Set to Interfacial Area Transport Equations for Gas–Liquid Two-Phase Flows

For the direct simulation of liquid atomization processes affected by surface tension, the level-set method was suitable, owing to the ease of estimating normal vectors and interface curvatures. However, the mass is not conserved in the original method because of errors in the interfacial advection evaluation. Therefore, previous studies have developed the interfacial advection equation and the interfacial evaluation method for reinitialization. The reinitialization method can be organized in terms of control parameters. Therefore, we modified and optimized the control parameters of the high-order constrained reinitialization scheme developed previously. Furthermore, the difference method in the convection term was adapted to the interfacial advection equation to evaluate the best method for simulating the droplet atomization process. Consequently, the fifth-order accuracy weighted essentially non-oscillatory scheme was observed to provide the best mass conservation for both the reinitialization and the advection equations.