Achievable Efficiency of Numerical Methods for Simulations of Solar Surface Convection

TL;DR

This paper evaluates the efficiency of numerical methods for simulating solar surface convection, demonstrating that higher-order schemes like WENO with Runge-Kutta are more accurate and computationally efficient.

Contribution

It compares various discretization schemes and identifies the most efficient combination for 3D stellar surface convection simulations.

Findings

WENO fifth order combined with second order Runge-Kutta is more accurate and efficient.

Error decay rates for different schemes are calculated for advective and diffusive problems.

SSP RK(3,2) is identified as the most efficient scheme for 3D simulations.

Abstract

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.