Explicit methods for the solution of the generalized Cauchy–Riemann equations and simulation of inviscid rotational flows

Abstract

Different levels of approximations for inviscid rotational flows are discussed. The generalized Cauchy–Riemann equations, consisting of the continuity equation and the definition of the vorticity are considered. Artificial time dependent terms are added to integrate the system to steady state. The system is also augmented with artificial viscosity terms for numerical stability and to avoid odd/even decoupling of central differences of first-order derivatives. Additional artificial viscosity is needed to capture shock waves. Explicit integration of the augmented system by two methods is studied. Numerical results for inviscid flow with non-uniform far field conditions are presented. Both methods are suitable for computation on parallel machines.