Optimization of time integration schemes coupled to spatial discretization for use in CAA applications

In this paper errors arising from spatial and temporal discretization are discussed. A new formulation to optimize time integration schemes is proposed. The new optimization also takes the errors coming from the spatial discretization into account, which leads to a minimization of the total errors. It is applicable to central and upwind type spatial discretizations. A six stage Runge–Kutta scheme is optimized for central and upwind spatial discretizations. Its efficiency is demonstrated on a one dimensional convection equation and on a Linearized Euler problem. The results indicate an important improvement.