압축성 유동 영역에서 Upwind 유한요소 방법들의 비교연구

Abstract

Upwind finite element schemes based on the Petrov-Galerkin method; SUPG by Brooks and Hughes, optimal upwind method by Chee and Kwon and exponential weighting function method by Kakuda and Tosaka, are compared in this paper to investigate the property of schemes and performances. The optimal upwind method is applied to the transonic flow and the exponential weighting function method is newly extended to the compressible flow region. The implemented schemes have the followings: Petrov-Galerkin formulation with an oscillation-free shock-capturing operator, structured grid and explicit time integration with local-time-stepping. These schemes are compared on the compressible flow problems. Further, the effect of control parameters on the accuracy is studied in some details and it reveals that the quality of solution is depended on the performance of the shock capturing of each method.