Low Dissipation E-CUSP Upwind Scheme Coupled Adaptive Order WENO Scheme And Its Application

Since the computer came out,it has been promoting the development and application of numerical calculation methods.There are many classical schemes in computational fluid dynamics(CFD).The invention or improvement of different schemes is almost centered on how to improve the calculation accuracy and reduce the time consumption.In order to improve the accuracy and efficiency of numerical simulation,the low dissipation E-CUSP upwind scheme coupled with adaptive order WENO method is studied in this paper.The main work is as follows:In this paper,a new scheme is proposed to couple the low dissipation E-CUSP upwind scheme with the weighted essentially non-oscillatory(WENO)scheme.In the spatial direction,it uses the low dissipation E-CUSP upwind scheme,and the WENO scheme is used to reconstruct its flux.Fourth-order total variation reduction(TVD)Runge-Kutta method is used in time direction.The governing equation is Euler equation.The numerical results of several examples show that the stability of the scheme is good,and the accuracy of the scheme,especially near the shock wave,is obviously improved.The combination of the E-CUSP scheme and the WENO scheme not only inherits the advantages of the E-CUSP upwind scheme,such as small computation and fast convergence,but also keeps the property of the WENO scheme stable at the discontinuity and essentially non-oscillatory.Secondly,in order to reduce the amount of calculation and improve the efficiency of calculation,we construct different precision adaptive order WENO-AO schemes:WENO-AO(5,3),WENO-AO(7,3)and WENO-AO(9,3).Then it is coupled with E-CUSP scheme for numerical simulation of Euler equations.The results show that the WENO-AO scheme has the same stability and robustness as the same order WENO scheme,but compared with the same order WENO scheme,the calculation efficiency of the 5th order WENO-AO(5,3)and 7th order WENO-AO(7,3)schemes is improved by 7.82%and 11.78%respectively for the classical shock tube calculation examples.Finally,the idea of constructing adaptive order WENO scheme is given by means of recursive method,taking WENO-AO(7,5,3)scheme as an example.A series of adaptive order WENO schemes can be constructed.The numerical results show that the construction method of recursive adaptive order WENO scheme is effective and feasible.The recursive adaptive WENO-AO(7,5,3)scheme shows higher stability.