Application of a new control-volume-based finite-element formulation to the shock tube problem

Abstract

Introduction I this article, the performance of a newly developed pressurebased method for incompressible/compressible flow calculation is investigated by solving the shock tube problem. This problem has served as a benchmark case in the literature,' since it has many transient flow features. Pressure-based methods have been increasingly used for the solution of compressible flow.' The present method is a generalized version of the method of Ref. 5, which was developed for incompressible flow computation, using primitive variables. Primitive-variable methods are widely used in the incompressible range. Here it is demonstrated that the present method is also very capable of solving transient and compressible flows incorporating strong discontinuities. The governing equations are discretized using a control-volumebased finite element (CVBFE) method. The CVBFE method was initially developed for the solution of heat transfer and fluid flow problems.' Later, its application to compressible flow computation was presented in the literature.' With the use of a new formulation for the mass conserving velocity (or convecting velocity), proposed by Karimian and Schneider, a strong coupling between pressure and velocity is created which does not allow any kind of checkerboard oscillations. The effect of three different methods for energy flux evaluation on the results are also examined in this article. The present results agree very well with the exact solution. No explicit artificial viscosity is added to the solution.