Verification of an entropic regularization method for discontinuous Galerkin schemes applied to hyperbolic equations

In this work, methods of entropic correction in numerical schemes for hyperbolic equations are extensively overviewed. The variational method of entropic regularization in discontinuous Galerkin schemes is tested on the one-dimensional gasdynamic Einfeldt problem of two scattering rarefaction waves. Based on the results of this test, a simplified method of entropic regularization in discontinuous Galerkin schemes coupled with a slope limiter is proposed. The designed method is successfully verified on a number of Riemann problems for one-dimensional Euler equations.