This research explores the static visibility problem, focusing on identifying visible regions in environments with fixed obstacles and a stationary viewpoint. The problem is formulated as the determination of visibility boundaries within the level set framework. To address this, a novel grid-based algorithm is introduced, designed to improve computational efficiency while maintaining high accuracy. This method integrates phase flow techniques, enables localized computations near the visibility interface with the growing method, and further reduces the computational burden associated with high-resolution grids with tube structures. Additionally, a new Heaviside function approximation, inspired by advanced Delta function methodologies, is proposed. This approach is conjectured to have second-order accuracy in calculating the volume of visibility regions. All accuracy and computational workload considerations are verified through numerical experiments.