Applications Of Osher-solomon Scheme Based On The Third Order WENO-Z For Hyperbolic Conservation Laws

Hyperbolic conservation laws are one kind of important models in computational fluid dynamics.One of the main characteristics of its numerical simulation is that whether their initial conditions are smooth or not,their solutions may be flattened in the discontinuous region.When solving the hyperbolic conservation laws,the Osher-Solomon scheme with low order accuracy can not simulate the exact solution accurately.Therefore,this paper reconstruct the values in cell interface of Osher-Solomon scheme by WENO-Z,and obtain a new Osher-Solomon scheme with high precision and resolution.Finally,we analyze the typical examples of Burgers equations and shallow water equations to verify the characteristics of the improved scheme.Specific research has been done in the following aspects:(1)In this paper,the conserved variables in cell interface of Osher-Solomon scheme are reconstructed by the WENO-Z3,then WENO-Z3 Osher-Solomon is obtained.The results show that the WENO-Z3 Osher-Solomon scheme has the characteristics of small error and high convergence order.(2)The WENO-Z3 Osher-Solomon scheme is applied to the numerical solution of one-dimensional and two-dimensional Burgers equations.The numerical results show that the ability of the new scheme to capture shock and sparse waves is better than that of Osher-Solomon scheme and WENO3 Osher-Solomon scheme.(3)The WENO-Z3 Osher-Solomon scheme is applied to the numerical solution of one-dimensional and two-dimensional shallow water equations.The numerical results show that the numerical solution of the new scheme is closer to the exact solution than that of the Osher-Solomon scheme and the WENO3 Osher-Solomon scheme.