An Improved Fifth-order WENO-Z Scheme And Its Numerical Simulation

High precision numerical simulation of complex flow field has always been one of the key research contents of computational fluid dynamics.For simulations that include discon-tinuous and complex flow fields,a high-precision and low-dissipation shock capture scheme is required.WENO-Z scheme is a scheme which not only can clearly and without oscillation capture the discontinuity,but also has a higher calculation accuracy in the smooth area.A large number of experimental results have shown that WENO-Z scheme has the problem of reduced accuracy at critical points.However,the analysis and discussion of Acker pointed out that for relatively coarse grids,the most critical way to improve the resolution of WENO scheme is to increase the weight on the non-smooth substentcils.Based on this idea,a high-precision and low-dissipation improvement WENO-Z scheme is constructed.The details are as follows:On the basis of the fifth-order WENO-Z scheme,the correction term?⁶)are added.A class of higher-order global smoothness indicators is constructed by linear combination of the three-point original and five-point global smoothness indicators.Two groups of different coefficient combinations are derived,and two improved the WENO-Z scheme（WENO-NP5scheme and WENO-RP5 scheme）are obtained.The parameters of the new scheme are de-termined by using the approximate dispersion relation（ADR）,It is found that when the WENO-NP5 scheme and WENO-RP5 scheme have6)=₁₂¹¹and6)=₆⁵respectively,the spec-tral property of the new scheme is significantly improved.In this paper,one dimensional Sod shock tube,two dimensional Riemann problem,Rayleigh Taylor instability and other classical examples are selected to carry out numerical experiments on the new scheme.The results show that the new scheme achieves fifth-order accuracy and maintains essentially non-oscillatory（ENO）property at discontinuities,those performs better than the WENO-Z scheme.