A High Resolution Finite Volume Scheme For One Dimensional Euler Equations

The Riemann problem of Euler equation is a typical one-dimensional conservation law system,which is often difficult to be solved analytically.However,low order linear precision scheme numerical dissipation is too large,high order accurate scheme does not satisfy the boundedness to non-physical oscillations.In order to solve the problem of non-physical oscillation.A new NVF high resolution scheme HRFVM(High Resolution Finite Volume Scheme)is constructed by using Hermite interpolation in the process of discretization of the linear convection term of the equation,which is based on the TVD criterion and the CBC-BAIR.The three order TVD type Rnge-kutta method is used to ensure the accuracy of the time.Through the typical examples to verify the accuracy of the new scheme.The exact solution of the linear convection equation is used to verify the accuracy of the new scheme.Compared with the CUI scheme,the new scheme is proved to be effective in suppress-ing the non-physical oscillations at discontinuities;Nonlinear equation of one-dimensional inviscid Burgers equation and the Buckely-Leverett problem,and further verify the ap-proximation effect of the scheme;Finally,the Lax shock tube problem and the Shu-Osher problem of one-dimensional Euler equation are solved,By comparing with the WENO5 scheme.the new scheme is proved to be effective.