Past studies show that until now the Random Vortex Method (RVM) has only been used to solve the flow of Newtonian fluids. In this paper, by presenting a new approach, the RVM is developed for the first time with the aim of simulating the flow of non-Newtonian fluids. For this purpose, a numerical simulation of two-dimensional flow of non-Newtonian power-law fluid in a T-junction is presented. The simulation is conducted for Re = 50-200 at the inlet of the channel and different power-law indexes (n = 0.2-1.4). The RVM solves the Navier–Stokes equations as a function of time and determines the velocity at any point of the channel directly and without determining a mesh on the geometry. Potential velocity, an initial condition for the flow analysis by the RVM, is obtained using the Schwarz–Christoffel conformal mapping. The effect of two parameters of power-law index and Reynolds number on the recirculation zone has been investigated. Acceptable agreement among the results of the present study and the existing numerical and experimental results shows the capability of the proposed method, according to which the VM can be considered a powerful promising method in simulating the non-Newtonian fluids in laminar and turbulent flow regimes.

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