Review for group velocity control schemes

The basic principles and the recent developments of group velocity control (GVC) method are reviewed. GVC method is a new shock capture method by controlling the dispersion error of numerical schemes. In GVC method, the “fast” scheme is used in front of the shock and the “slow” one is used behind the shock, and in this way, the spread of numerical oscillations is limited in a very small region near the shock, and thus the oscillations are suppressed. The GVC method capture shock mainly by using dispersion technique, therefore, the dissipation of GVC schemes is relatively low. The recently developments of GVC schemes, such as compact GVC scheme, optimized GVC scheme, hybrid weighted GVC-WENO scheme and GVC scheme by group velocity booster, are also reviewed. GVC schemes are useful methods for detail simulation of multi-scale flows.