  We investigate the achievable efficiency of both the time and the space
discretisation methods used in Antares for mixed parabolic-hyperbolic problems.
We show that the fifth order variant of WENO combined with a second order
Runge-Kutta scheme is not only more accurate than standard first and second
order schemes, but also more efficient taking the computation time into
account. Then, we calculate the error decay rates of WENO with several explicit
Runge-Kutta schemes for advective and diffusive problems with smooth and
non-smooth initial conditions. With this data, we estimate the computational
costs of three-dimensional simulations of stellar surface convection and show
that SSP RK(3,2) is the most efficient scheme considered in this comparison.
