Discontinuous Galerkin method with entropic slope limiter for Euler equations

The variation approach to obtaining equations of entropy stable discontinuous Galerkin method is generalized. It is shown how monotonicity property can be incorporated into this approach. As applied to Euler equations, the entropic slope limiter, a new effective approximate method for the problem of the studied approach, is designed. It guarantees monotonicity of the numerical solution, non-negativity of pressure and entropy production for each finite element. This method is successfully tested on some well-known gas dynamics model problems.