No 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.

The conventional meshless local Petrov–Galerkin method is modified to enable the method to solve turbulent convection heat transfer problems. The modifications include developing a new computer code which empowers the method to adopt nonlinear equations. A source term expressed in terms of turbulent viscosity gradients is appended to the code to optimize the accuracy for turbulent flow domains. The standard [Formula: see text] transport equations, one of the most applicable two equation turbulent viscosity models, is incorporated, appropriately, into the developed code to bring about both versibility and stability for turbulent natural heat transfer applications. The amenability of the new developed technique is tested by applying the modified method to two conventional turbulent fluid flow test cases. Upon the obtained acceptable results, the modified technique is, next, applied to two conventional natural heat transfer test cases for their turbulent domain. Based on comparing the results of the new technique with those of the available experimental or conventional numerical methods, the proposed method shows good adaptability and accuracy for both the fluid flow and convection heat transfer applications in turbulent domains. The new technique, now, furthers the applicability of the mesh-free local Petrov-Galerkin (MLPG) method to turbulent flow and heat transfer problems and provides much closer results to those of the available experimental or conventional numerical methods.