<p>In the field of discretization-based meshfree/meshless methods, the improvements in the higher-order consistency, stability, and computational efficiency are of great concerns in computational science and numerical solutions to partial differential equations. Various alternative numerical methods of the finite particle method (FPM) frame have been extended from mathematical theories to numerical applications separately. As a comprehensive numerical scheme, this study suggests a unified resolved program for numerically investigating their accuracy, stability, consistency, computational efficiency, and practical applicability in industrial engineering contexts. The high-order finite particle method (HFPM) and corrected methods based on the multivariate Taylor series expansion are constructed and analyzed to investigate the whole applicability in different benchmarks of computational fluid dynamics. Specifically, four benchmarks are designed purposefully from statical exact solutions to multifaceted hydrodynamic tests, which possess different numerical performances on the particle consistency, numerical discretized forms, particle distributions, and transient time evolutional stabilities. This study offers a numerical reference for the current unified resolved program.</p>