Three-Directional Orthogonality Preserving Method for Hyperbolic Grid Generation

The hyperbolic grid generation method is widely used for generating computational grids. Because of conflicts arising from various grid constraints, the traditional hyperbolic grid generation method faces challenges in guaranteeing the fulfillment of all orthogonal constraints among three directions during the grid generation. A new three-directional orthogonality preserving method (TDOP) is introduced in the present work to enhance the orthogonality of the computational grid during the grid generation process. Unlike the traditional grid generation method, TDOP takes all three orthogonal constraints into consideration, establishes a function to quantify the overall grid orthogonality, and subsequently derives new governing equations for grid generation by solving a constrained optimization problem. Compared with the traditional method, TDOP exhibits enhanced control over the orthogonality among three directions, thereby enabling the generation of a computational grid with better orthogonality. Three application cases are employed to demonstrate the effectiveness and superiority of TDOP in hyperbolic grid generation. Results indicate that, compared with the traditional method, TDOP can effectively prevent the emergence of highly skewed grids and enables enhanced optimization of orthogonality in the advancing front layer. Consequently, TDOP can generate a computational grid with better orthogonality and higher quality than the traditional method.