SOME REMARKS ABOUT THE RESOLUTION OF HIGH-VELOCITY FLOWS NEAR LOW-DENSITIES

High velocity flows which are exposed to strong rarefaction waves and creating low densities regions in it present difficulties and inaccura cies for numerical resolution. In particular, variables related to the internal energy are wrongly evaluated. Use of classical schemes solvi ng the Euler equations in conservative variables introduces significan t errors in the determination of temperature. We recommend to employ a non-conservative formulation of the energy equation. Results found to be more accurate in using the present internal energy formulation. In order to have the formulation available for both shock and strong rar efaction waves, we propose a hybrid formulation of conservative and no n-conservative ones, depending on a shock indicator. The results are c ompared with exact solutions and show a significant improvement of the accuracy. The method is then extended to two-dimensional cases.