Non-reflecting coupling method for one-dimensional finite difference/finite volume schemes based on spectral error analysis

For the compressible coupled simulation of piping systems including fluid machinery, an embedment of 3D finite volume schemes for active components such as pumps and compressors into 1D finite difference characteristic methods for passive components (e.g. pipes, valves) offers a sophisticated 3D investigation of the machinery with a moderate simulation effort for the entire system. While a 3D-1D coupling method for finite volume Godunov schemes is available from preliminary studies, in the present paper, a new non-reflecting coupling method for 1D finite volume Godunov and 1D finite difference characteristic methods is presented, and the mechanisms for spurious reflections at the coupling interface are revealed. The proposed methodology is based on spectral error analysis and is in general applicable to the coupling of any fundamentally different numerical schemes. It is demonstrated that by matching the numerical diffusion and speed of sound in both coupled domains, reflections can be minimized.