A key idea finite difference weighted essentially nonoscillatory(WENO)schemes is a combination of lower order fluxes to obtain a higher order approximation.The choice of the weight to each candidate stencil,which is a nonlinear function of the grid values,is crucial to the success of WENO.For the system case,WENO schemes are based on local characteristic decompositions and flux splitting to avoid spurious oscillatory.But the cost of computation of nonlinear weights and local characteristic decompositions is very expensive.