An Approach Of High Order Numerical Flux

According to the MUSCL format construction idea,this paper presented a high-order numerical flux construction method.It is applied to the finite volume(difference)ENO,WENO and DG schemes to obtain the corresponding single-step high-order Semi-Lagrangian schemes.For the one-dimensional piecewise linear inviscid Burgers equation,a kind of flux accurate value is given and the properties of this high-order numerical flux are discussed.Combined with the SSP Runge-Kutta method,single-step second-order scheme using second-order numerical fluxes is generalized to the two-step-third-order scheme.Numerical experiments show that the new scheme has smaller error and higher efficiency than the original scheme,and the simulation effect of shock wave and sparse wave is also greatly improved.For the one-dimensional Euler equations,this paper presented a new characteristic line processing method in the feature space.The FD format combined with the alternating direction method based on this method can be directly applied to the multi-dimensional Euler equations,and there is no need to give different Riemann invariants according to the problem.The one-step high-order Semi-Lagrangian scheme in this paper numerically simulates the one-dimensional Riemann problem.The result is higher resolution and efficiency than the original scheme(keeping the spatial discrete scheme,time dispersion with the corresponding SSP Runge-kutta scheme).Through the numerical simulation of the two-dimensional Rayleigh-Taylor instability problem,the practicability and effectiveness of the new scheme can be verified.