Linear-stream preserving finite difference method on curvilinear grids

Finite difference methods (FDMs) on curvilinear grids struggle to maintain numerical accuracy due to grid non-uniformity, even when satisfying the requirement of free-stream preservation. To address this issue, we introduce the concept of linear-stream preservation and propose a novel FDM framework based on the discrete equivalence equation and its discrete rule. The proposed method employs a gradient-based interpolation scheme, effectively mitigating spatial coupling errors introduced by traditional interpolation methods. Numerical examples, including linear-stream preservation, isentropic vortex, subsonic channel flow, and supersonic flow past a cylinder, demonstrate that the proposed method significantly reduces numerical errors and enhances computational stability on non-smooth grids. The proposed linear-stream preserving FDM offers substantial advantages in grid adaptability, paving the way for more reliable and robust FDM-based computational fluid dynamics simulations on complex geometries.