Meshless Method for Numerical Solution of Internal Flows with Axial Symmetry

In this research, a meshless method has been developed to solve internal and axi-symmetric flows. In this method, the least squares of the Taylor series are used for spatial discretization and explicit multi-step Runge-Kutta method is used for temporal discretization. Governing equations are based on two-dimensional and axi-symmetric Euler equations. The second and forth order dissipation are used to solve the flows. In order to model boundary condition, subsonic and supersonic inlet and outlet boundary conditions as well as the wall boundary have been used according to the problem. To validate the results of the code, the inviscid flow inside a two-dimensional nozzle and the supersonic flow inside the channel along with bump have been simulated and the results have been compared with valid data. Also, the ability of the code to shock capturing in the two-dimensional and axi-symmetrical nozzle is presented. Finally, the simulation of the steady flow inside a axi-symmetric convergent-divergent supersonic nozzle with Mach 5 in outlet has been done to measure the accuracy of solving the numerical code at hypersonic speed. The results show that the developed code can simulate steady internal and axi-symmetric flows with very good accuracy. The code convergence process is also presented, which shows appropriate convergence of the developed code. The analysis time for shock capturing in the axisymmetric nozzle is about 64% faster than the Fluent-software.