Optimization of phase field variables in gas-liquid two-phase flow problems

Sugihara, Kenta ; Onodera, Naoyuki   ; Idomura, Yasuhiro   ; Yamashita, Susumu   

The phase-field method has been successfully applied to various multi-phase flow problems as an interface tracking method for gas-liquid interfaces. However, the accuracy of the phase-field method depends on hyper-parameters, which are empirically adjusted for each problem. The phase-field method sustains sharp interfaces by the balance between the numerical viscosity of the advection term and the interface modification by the diffusion and anti-diffusion terms. Based on this fact, we propose a method for deriving the optimal hyper-parameters in a non-empirical manner by performing a basic error analysis of the interface advection.