A nearly-monotone genuinely multidimensional scheme for the Euler equations

Recent progress made in the development of a genuinely multidimensional finite-volume method for the Euler equations is reported. In this method, wave information is derived from a reconstruction procedure applied to the data on a triangle. The algorithm is therefore best suited to application on an unstructured grid. A flux formula which provides nearly-monotone solutions is also presented. The new method is tested on three simple 2D flows, and the results show that dominant-wave resolution is high, and that strong-wave transitions are nearly monotone.