Comparison of WENO and HWENO Limiters for the RKDG Method Implementation.

The results of comparative study of the WENO-type monotonization methods for numerical solution of the Euler equations computed by the discontinuous Galerkin method are presented. The variants of the technique based on Lagrangian and Hermitian interpolation are analyzed. 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. [ABSTRACT FROM AUTHOR]