Accelerated calculation of phase-variable for numerical simulation of multiphase flows

In this manuscript, we unveil an innovative acceleration technique for the simulation of multiphase flows, which builds upon the foundation laid by our previously devised multiphase flow solver. The cornerstone of this method lies in augmenting computational efficiency through the selective updating of variables solely within domains characterized by significant gradients of the phase variable. This tactic diminishes the dimensionality of the system of linear equations, thereby hastening the computational process. To pinpoint the regions warranting focused attention, a judicious criterion is indispensable to strike an optimal balance between efficiency and precision. This criterion affords a marked decrement in computational expenditure while preserving the fidelity of the original methodology. Rigorous validations corroborate that this acceleration mechanism can enhance computational efficiency by a minimum of 49.5% in resolving the phase field equation and by at least 70.2% in the computation of pragmatic two-phase flows, without compromising accuracy. Moreover, the efficacy of this acceleration technique is inversely proportional to the rate of interface evolution, becoming increasingly efficient as the interface evolves more slowly.