Second order front tracking for the Euler equations

A second order front tracking method is developed for solving the hyperbolic system of Euler equations of inviscid fluid dynamics numerically. Meshless front tracking methods are usually limited to first order accuracy, since they are based on a piecewise constant approximation of the solution. Here second order convergence is achieved by deriving a piecewise linear reconstruction of the piecewise constant front tracking solution. The linearization is performed by decomposing the front tracking solution into its wave components and by linearizing the wave solutions separately. In order to construct a physically correct linearization, the physical phenomena of the front are taken into account in terms of the front types of the previously developed improved front interaction model. This front interaction model is also extended to include front numbers used in the wave decomposition. It is illustrated numerically for Sod’s Riemann problem, the two interacting blast waves problem, and a two-dimensional supersonic airfoil flow validation study that the proposed front tracking method achieves second order convergence also in the presence of strong discontinuities and their interactions.