Numerical analysis of Newtonian flows based on artificial compressibility AC method

Abstract

      In this study, numerical analysis for incompressible Newtonian flows has been conducted by using an artificial compressible method ( -method) based on the Galerkin finite element approach. As well known, Naiver-Stoke partial differential equations are employed to describe activity of the fluid. This model, which consists of two differential equations; named the conservation of mass and time-dependent conservation of momentum is presented in cylindrical coordinates system (Axisymmetric flow). The effects of many factors such as Reynolds number ( ) and artificial compressibility parameter ( ) are discussed in the present study. In particular, this study emphasized on the impact of these parameters on the level of convergence. To satisfy the analysis of the method, Poiseuille flow along a circular conduit under isothermal condition is utilized as a simple test problem. This test is conducted by taking a circular cross section of pipe.