압축성 유동 모사를 위한 셀중심 유한체적 기법용 출구 무반사 특성경계조건에 관한 연구

Abstract

A non-reflecting boundary condition is known to be an essential element for compressible flow simulations unless the computational domain is infinitely large. Practical engineering applications involve a finite domain yet complex nature of which discretization favors a finite-volume method (FVM) over a finite-difference method (FDM) in terms of computational cost and efficiency. A non-reflecting characteristic boundary condition (CBC) is implemented in a cell-centered compressible finite-volume solver. While the CBC is well-suited for FDM and vertex-based FVM, the implementation in a cell-centered FVM causes a subtlety due to the mistmatch between the cell-center and the boundary face center. Motivated by Nordström & Björck (2001, Applied Numerical Mathematics), we first introduce the data node at the boundary face center, and then integrate the governing equations modified by the characteristic approach as Granet et al. (2010, AIAA) used for the vertex-based FVM. An alternative approach similar to Motheau et al. (2017, AIAA) that utilizes spatial derivatives modified by the characteristic approach instead of time-integration is also implemented. Two different implementations are compared for a canonical convecting inviscid vortex problem and the effect of numerical dissipation of boundary fluxes and grid resolution sensitivity on the test are also examined. Finally CBC implementations are tested on the VKI turbine cascade against the experimental data.