지수가중함수를 이용한 압축성 유동의 Upwind 유한요소해석

Abstract

A new upwind finite element formulation for the first-order hyperbolic systems with particular emphasis on the one dimensional compressible Euler equations is presented. The basis of formulation is the exponential weighting function suggested by Shen and the Jacobian matrix of flux vectors to define the perturbation of the weighting function suggested by Tezyduar. The exponential weighting function for linear element is combined with the Streamline-Upwind/Petrov-Galerkin(SU/PG) concept. The accuracy is demonstrated on several example problems and compared with other methods. The present results show that the scheme with the exponential weighting function is much better than the SU/PG in discontinuity capturing. Comprehensive computational results for isothermal nozzle flows are presented and compared with the Taylor-Galerkin method and the SU/PG method. The results are in good agreement with the exact solutions. However, a treatment for suppression of small oscillations near the shock remains for the future work.