A Numerical Study Of The Trigonometric WENO Scheme Based On Different Numerical Fluxes

Hyperbolic conservation laws are widely used in ma.ny fields.Constructing effective numerical schemes to solve hyperbolic conservation laws is an important research direction of computational fluid dynamics.However,for some non-linear hyperbolic conservation laws,even if the initial conditions are smooth enough,the solution may be discontinu-ous after a period of evolution,which puts forward high requirements for our numerical schemes.Weighted essentially non-oscillation(WEND)schemes are a class of numerical schemes widely used to solve hyperbolic conservation laws.These schemes can obtain high order accuracy in smooth regions and escape spurious oscillations adjacent to strong shocks or contact discontinuities.In this paper,we further explore the new type of finite volume WENO scheme[1]for solving hyperbolic conservation laws,which mainly includes two aspects.On the one hand,because numerical methods based on trigonometric polynomial functions appear to be very suitable for the simulation of some highly oscillatory problems or wave-like phenomena,trigonometric polynomial reconstruction is used instead of algebraic polyno-mial reconstruction as the building block of finite volume WENO scheme.On the other hand,because of the simplicity of Lax-Friedrichs(LF)numerical flux,LF numerical flux is used in most papers concerning numerical fluxes.Besides,there are some other nu?me.rical fluxes,including the first-order monotone numerical fluxes such as the Godunov numerical flux,the Engquist-Osher numerical flux,etc.,and the second-order TVD fluxes.We systematically investigate the performance of the finite volume trigonometric WEND(TWENO)scheme based on different,numerical fluxes with the objective of obtaining better performance by choosing suitable numerical fluxes,addressing the issues of CPU cost,error,accuracy,nonoscillatory property,and resolution of discontinuities.