Extending the Meshless Local Petrov–Galerkin Method to Solve Stabilized Turbulent Fluid Flow Problems

Abstract

The aim of this paper is to extend the meshless local Petrov–Galerkin method to solve stabilized turbulent fluid flow problems. For the unsteady incompressible turbulent fluid flow problems, the Spalart–Allmaras model is used to stabilize the governing equations, and the meshless local Petrov–Galerkin method is extended based on the vorticity-stream function to solve the turbulent flow problems. In this study, the moving least squares scheme interpolates the field variables. The proposed method solves three standard test cases of the turbulent flow over a flat plate, turbulent flow through a channel, and turbulent flow over a backward-facing step for evaluation of the method’s capability, accuracy, and validity purposes. Based on the comparison of the three test cases results with those of the experimental and conventional numerical works available in the literature, the proposed method shows to be accurate and quite implemental. The new extended method in this study together with the previously published works of the authors (on extending the meshless local Petrov–Galerkin method to solve laminar flow problems) now, for the first time, empower the meshless method to solve both laminar and turbulent flow problems.

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