Enhanced partial donor cell method for hyperbolic equations in orthogonal curvilinear coordinates

An enhanced high-order reconstruction method for finite-volume solvers in orthogonal curvilinear coordinates is presented. Extending the classical Partial Donor Method (PDM) to account for geometric effects, the scheme achieves arbitrary high-order convergence while preserving monotonicity and minimizing numerical diffusion. Optimal seventh-order interpolation formulas for uniform cylindrical and spherical-radial grids are derived, complemented by an optional non-clipping algorithm that enhances accuracy near narrow extrema. Extensive tests in both linear and non-linear systems validate the method's high spatial accuracy and non-oscillatory performance. Its straightforward derivation and modest computational overhead render the approach a promising tool for astrophysical, space, and planetary applications, with the potential for extension to other curvilinear systems.