A Second Order Front Tracking Solution of the Euler Equations

A second order front tracking method is developed for solving the Euler equations of inviscid fluid dynamics numerically. Front tracking methods are usually limited to first order accuracy, since they are based on a piecewise constant approximation of the solution. Here the second order convergence is achieved by building a piecewise linear reconstruction of the piecewise constant front tracking solution in a post-processing step. The linearization is performed by decomposing the piecewise constant solution of the hyperbolic system into its wave components and by linearizing the wave solutions separately. In order to achieve a physically correct linearization, the front types of the previously developed improved front tracking method are employed. It is illustrated numerically for the one-dimensional unsteady interacting blast waves problem and a two-dimensional supersonic airfoil flow validation study that the proposed front tracking method can achieve second order convergence also in the presents of strong discontinuities.