Generalized Split-Explicit Runge–Kutta Methods for the Compressible Euler Equations

The compressible Euler equations exhibit wave phenomena on different scales. A suitable spatial discretization results in partitioned ordinary differential equations where fast and slow modes are present. Generalized split-explicit methods for the time integration of these problems are presented. The methods combine explicit RungeKutta methods for the slow modes and with a free choice integrator for the fast modes. Order conditions for these methods are discussed.