SUPG finite element method for adiabatic flows

Abstract

The purpose of this paper is to present the SUPG finite element method for adiabatic flows and to compare the results with those obtained via various computational methods. The incompressibility assumption is often used to solve transient viscous flows. On the other hand, compressible flow analyses are also popular because natural flows include compressibility even if it is a negligible amount. It is well known that incompressibility is a limit state of compressibility. To solve compressible flows, three kinds of governing equations are needed: the conservation of mass, momentum, and energy, in which density, velocity, and internal energy are independent variables. If we assume that there is no heat transfer in or out of a system, the energy equation can be eliminated from the governing equations. Density and velocity can be considered independent variables. These kinds of flows are referred to as adiabatic flows in this paper.The SUPG formulation is one of the most widely used methods in the finite element analyses of fluid flows. In this paper, the SUPG method for adiabatic flows is presented. The polytropic law is introduced for the equation of state. Moreover, the computational results obtained by four models of fluid flows are compared: adiabatic flows, compressible flows, constant acoustic velocity flows, and incompressible flows. Verifications are carried out using a lid-driven cavity flow. Boundary effects are estimated using a wide computational domain. Drag forces are compared with those computed using incompressible flows. The pressure coefficients over a surface of a circular cylinder located in fluid flows computed by the present method show good correspondence with the experimental measurement. On the other hand, significant discrepancies are observed between the pressure coefficients computed assuming constant density and the experimental results.