Structured Orthogonal Curvilinear Grid Generation for Arbitrary Boundaries

In computational fluid dynamics and finite element analysis, the generation of orthogonal curvilinear grids serves as a critical pre-processing step. Traditional rectangular grids struggle to adapt to complex boundary shapes, whereas structured orthogonal curvilinear grids for arbitrary boundaries can better conform to physical contours, thereby improving computational accuracy.

The defining characteristic of orthogonal curvilinear grids lies in their grid lines maintaining perpendicular intersections while perfectly conforming to irregular boundaries. These grids are typically generated using differential equation methods, achieved by solving elliptic partial differential equations (such as Poisson's equation) to establish boundary-to-computational-domain mapping transformations. The core algorithm involves numerically solving Poisson equations with boundary-fitted coordinates using finite difference methods, where source terms control grid orthogonality and spacing distribution.

The key advantage of this implementation is the simplification of complex traditional grid generation workflows. Users only need to input geometric boundary information, and the program automatically performs grid orthogonality optimization and internal node distribution adjustment. The generated grids maintain boundary conformity while ensuring numerical stability through orthogonality control. The code implementation typically includes boundary discretization modules, elliptic equation solvers with adaptive source terms, and orthogonality correction algorithms that iteratively adjust grid line angles.

Typical application scenarios include: Body-fitted grid generation for airfoil flow analysis Meteorological simulations over complex terrains Tissue boundary fitting in biomedical modeling The grid generation approach eliminates the tedious manual parameter adjustment steps required in traditional methods, allowing researchers to focus more on the physical problems themselves rather than pre-processing tasks. The implementation often features automatic grid quality metrics calculation and visualization modules for immediate validation of orthogonality and smoothness properties.