The structure which represents the connectivity of mesh using hexa and tetra for the purpose of solving equation at nodal location of domain structure. Analyzing simulation of IC engine structure meshing is the first step to solve and ensure the result is based on the high-quality mesh to prove with efficient terms in required time. The equivalence relation between automatic mesh in IC engine with different mesh technique and meromorphic quadratic differentials is discovered in this paper. Each automated mesh generates a conformal surface structure like tringle, square is identified with mermorphic quadratic differential, in which the configuration of singular vertices corresponds to the configuration of the meromorphic differential's poles and zeros(divisor). Due to We obtain co-efficient boundaries using Riemann surface theory, and a constructive algorithm for meromerphic quadratic differential on category zero surfaces is proposed. Our experimental results demonstrate the efficiency of the mesh with default, hexa, tetra and proximity for solving the algorithm with meromorphic quadratic analysis. This opens up a direction for automatic mesh generation using algebraic geometric approach. © 2023 Elsevier B.V., All rights reserved.