Higher-order explicit schemes based on the method of characteristics for hyperbolic equations with crossing straight-line characteristics

摘要

We develop method of characteristics schemes based on explicit Runge-Kutta and pseudo-Runge-Kutta third- and fourth-order solvers along the characteristics. Schemes based on Runge-Kutta solvers are found to be strongly unstable for certain physics-motivated models. In contrast, schemes based on pseudo-Runge-Kutta solvers are shown to be only weakly unstable for periodic boundary conditions and essentially stable for the more physically relevant nonreflecting boundary conditions. Our implementation of nonreflecting boundary conditions does not rely on interpolation.