Comparative study of WENO and Hermite WENO limiters for gas flows numeriсal simulations using the RKDG method

A comparative study of WENO-type monotonization methods for numerical solution of 1D gas dynamics equations system obtained by using discontinuous Galerkin method is presented. The Lagrangian and Hermitian interpolation-based variants of the technique are considered. Test simulations for the Sod problem, which solution contains a shock wave, a rarefaction wave, and a contact discontinuity, are performed. The merits and demerits of the considered variants of the limiters including the questions of the numerical solution monotonicity, numerical dissipation magnitude, computational costs and extensibility of software implementation are investigated.