Precise and analytical calculation of interface surface area in sharp interfaces and multiphase modeling

•A method to accurately calculate interface surface area within a computational cell is proposed.•The method is analytical and improves accuracy by one order of magnitude relative to the conventional VOF gradient method.•The proposed method allows a direct mass transfer calculation from fundamental principles of phase-change eliminating the need for empirical coefficients.•The method improves the simulation of multiphase flows by suppressing parasitic velocities.•The method improves the numerical prediction of heat transfer near the interface.