Abstract:
This paper considers Discontinuous Galerkin schemes based on Legendre polynomials of
degree $K=2, 3$. Schemes are written to solve the one-dimensional Hopf equation. Unsteady solution is acquired with ADER and Runge-Kutta algorithms. The high order of
numerical approaches is affirmed. The ADER method computational efficiency is studied
in comparison with traditional approach. Tests that are used are with an analytical solution (linear solution and running half-wave), and with Burgers turbulence. The result of
this work can be used to speed up 3D DG-based algorithms.