The Research On Low-Dissipation E-CUSP Upwind Scheme Coupling High-Precision WENO Algorithm

With the development of computer technology,Computational Fluid Dynamics(CFD),especially the numerical calculation method as the core technology of CFD,has been rapidly developed and widely applied.Although there are many classic schemes,how to improve the computational accuracy and efficiency of CFD is still a difficult problem that has puzzled people for a long time,and it is also the focus of academic circles.In order to improve the computational accuracy and efficiency of CFD,low-dissipation E-CUSP upwind scheme coupling high-precision weighted essential oscillation-free(WENO)method is studied based on finite volume method in this paper.Firstly,the performance of the low-dissipation E-CUSP upwind scheme is analyzed by comparing it with the Roe scheme.The governing equation is a one-dimensional Euler equation,the low-dissipation E-CUSP upwind scheme is adopted in space,and the explicit fourth-order Runge-Kutta propulsion method is adopted in time.The numerical results of two examples show that E-CUSP upwind scheme can effectively capture shock waves and contact discontinuity.Compared with Roe scheme,E-CUSP scheme costs less computer time and has higher computational efficiency.This is because E-CUSP upwind scheme decomposes non-viscous flux into conservation flux and pressure flux,which avoids matrix operation and makes this scheme have obvious advantages of small computation and good robustness.Secondly,the low-dissipation E-CUSP upwind scheme coupling high-precision weighted essentially oscillation-free(WENO)method is studied.In order to capture shock waves with high quality,low-dissipation E-CUSP upwind scheme is coupled with third-order and fifth-order WENO scheme respectively to simulate Euler equation due to the phenomenon of shock wave flattening in upwind scheme.The numerical results show that E-CUSP upwind scheme coupling WENO method can improve the accuracy of the scheme,especially the accuracy of the scheme near the shock wave.In this paper,the low-dissipation E-CUSP upwind scheme is combined with WENO,which not only inherits the advantages of E-CUSP upwind scheme,such as small computation and fast convergence,but also maintains the stable nature of WENO scheme in the discontinuous region with no oscillation in nature.Finally,a preliminary study on adaptive order WENO method is carried out.Due to the lack of robustness and computational complexity of the high-order WENO scheme,this paper makes a preliminary exploration of the adaptive order WENO method.The idea is to use low-order WENO scheme in the relatively smooth area of the flow field and high-order WENO scheme near the shock wave.Numerical results show that the adaptive order WENOmethod is efficient and accurate.