Roe の近似 Riemann solver の収束性に関する一考察

抄録

A three-dimensional Euler code for cascade flow calculation which is accurate and robust with good convergence property has been developed to investigate unsteady flow phenomena such as rotating stall or surge. The time-dependent Euler solvers provide a single approach for subsonic, transonic and supersonic flows, and have inherent shock-capturing capability. Consequently, they can provide important information on flow field such as shock location and pressure distribution. Moreover, they form a very essential part of Navier-Stokes solvers. In this research, the code is developed based upon a non-MUSCL-type TVD scheme using Roe's approximate Riemann solver. During this development, an insight which we consider to be quite important in the numerical simulations has been obtained. There exists ambiguity in the derivation of “Roe's averaging” on density. Our research has revealed that inappropriate use of this averaged density is not only analytically incorrect, but can have detrimental effects on flow calculation based upon Roe's approximate Riemann solver, especially when this averaged density is used in conjunction with unphysical eigen vectors of the Jacobian matrix of flux. The reason why this occures is fully discussed. The example for such a case is illustrated. Also, in order to show the quality of the developed code, the result of a transonic compressor rotor cascade at its design point is presented.