Application of the RKDG method for gas dynamics problems

In recent years the RKDG method with discontinuous basic functions which is characterized as a higher-order method is widely used. It’s known that for guaranteeing the monotony of solution obtained by this method it is necessary to use limiters especially if the solution contains big instabilities. However, application of limiters can negatively affect the accuracy of the solution. In this paper the way of saving the order of accuracy of the solution and guaranteeing the monotony is explored.