Meshless local Petrov–Galerkin method-higher Reynolds numbers fluid flow applications

The meshless local Petrov–Galerkin (MLPG) primitive variable based method is extended to analyze the incompressible laminar fluid flow within or over some different two-dimensional geometries. Although still in laminar regions, the Reynolds numbers considered in this study are in the ranges for which, in the literature, the MLPG primitive variable based method has never produced stable solutions and comparable results with those of the conventional methods. The considered test problems include, a steady lid-driven cavity flow with Reynolds numbers up to and including 10,000, a flow over a backward-facing step at 800 Reynolds number, and a transient fluid flow past a circular cylinder with Reynolds numbers up to and including 200. The present method solves the incompressible Navier–Stokes (N–S) equations in terms of the primitive variables using the characteristic-based split (CBS) scheme for discretization. The weighting function in the weak formulation of the governing equations is taken as unity, and the field variables are approximated using the moving least square (MLS) interpolation. For validation purposes, the obtained results are compared with those of the conventional numerical methods. The agreements of the compared results reveal a step forward towards further applications of the MLPG primitive variable based approach.