Development of Algorithm for Newtonian Compressible Fluid Flow Based on Finite Element Method

Abstract

In this article, we present the numerical investigation for compressible Newtonian flow in two dimensional axisymmetric channel. Galerkin finite element method is applied to accommodate compressible and incompressible flows. A continuity equation and time-dependent conservation of momentum equations are used to describe the motion of the fluid, which are maintained in the cylindrical coordinate system (axisymmetric). To meet the method analysis, Poiseuille flow along a circular channel under an isothermal state is used as a simple test problem. This test is conducted by taking a circular section of the pipe. Comparision between compressible and incompressible results in terms of convergence has been conducted for axial velocity and pressure. Findings reveal that, convergence-rates of velocity and pressure is faster an incompressible case compared to compressible. In addition, the level of  velocity convergence is higher than pressure for both compressible and incompressible. Moreover, the low level of Mach number demonstrates that piecewise-constant density interpolation is equitable to linear density interpolation.