Investigation of generalized Couette hydromagnetic flow of two-step exothermic chemical reaction in a channel via the direct meshless local Petrov–Galerkin method

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This paper concerns to propose a high-order local meshless method to simulate the Couette flow based on the incompressible Navier–Stokes equation and the generalized Couette hydromagnetic flow of two-step exothermic chemical reaction in a channel. The numerical solution is performed in the two main stages. First, time variable of the incompressible Navier–Stokes equation is approximated by a finite difference scheme as in this procedure, the velocities in x- and y-directions must be updated by using an explicit difference formula. Also, the pressure component is calculated by solving a Poisson’s equation in each time step. Here is the second stage e.g. a local meshless method based on the direct meshless local Petrov–Galerkin method is employed to solve the Poisson’s equation which corresponds to the pressure value. Some famous phenomena such as Couette flow are studied by using the proposed numerical algorithm. The results show that the new numerical procedure not only has suitable and acceptable accuracy but also it simply solves such interesting models. Up to the best of our knowledge, this is the first time that the direct meshless local Petrov–Galerkin method is applied for these problems and it can have more accuracy than other meshless methods.