Entropic regularization of the discontinuous Galerkin method for two-dimensional Euler equations in triangulated domains

An entropic regularization of the discontinuous Galerkin method in conservative variables is constructed for the two-dimensional Euler equations in domains divided into non-regular triangular cells. Based on the use of local orthogonal linear basis functions in a triangular cell, a new slope limiter is proposed. In order to ensure the fulfillment of the discrete analogue of the entropic inequality in a triangular cell, a special slope limiter is constructed.