Numerical Analysis of Density Changing Flows using the Semi-Lagrange Galerkin Method

The purpose of this paper is an analysis of adiabatic flows using the semi-Lagragian Galerkin method. In the study presented in this paper, conservations of mass and momentum of the adiabatic flows are employed as the governing equations. The BirchMurnaghan equation is assumed for the equation of state. The semi-Lagrange method is used, in which the governing equations are divided into the advection and nonadvection calculations. The advection calculation is transformed using the characteristic method. In both advection and non-advection calculations, the Hermite interpolation function which is complete third order approximation for a triangular element is used for both the velocity and density.