In this paper, the Newtonian incompressible Navier-Stokes equations in cylindrical polar coordinates can be solved using a Galerkin finite element method proposed based on an artificial compressibility scheme. In this study, two various formulations of the viscous stress tensor are represented, named the rate of deformation tensor T_rd and the velocity gradient tensor T_gv. A comparison is undertaken between both options T_rd and T_gv. In this context, attention is paid to the rate of convergence and the influence of variation in Reynolds number (Re) and artificial compressible parameter β_ac by using both assumptions, T_rd and T_gv. The critical values of Reynolds number (Re) and artificial compressible parameter β_ac are highlighted in this study as well. Generally, through the analysis of results, we detected that the results with the rate of deformation tensor T_rd are better than the results with the velocity gradient tensor T_gv.
A comparison of numerical solutions based on two different rates of deformation tensors by using the artificial compressibility method
Finite Element Method
Galerkin Method
Artificial Compressibility Method
Newtonian Flow
Navier-Stokes