accurate eno-like schemes for the model of fluid flows in a nozzle with variable cross-section

A class of accurate high-order $eno$-like schemes for the model of fluid flows in a nozzle with variable cross-section is presented. the model contains a nonconservative source term, which causes unsatisfactory results to standard numerical schemes, even for low-order ones. the proposed schemes rely on exact riemann solvers and the reconstructed piecewise polynomials which are nonoscillatory. these schemes inherit the high-order precision of the $eno$ schemes like many existing $eno$-type schemes, and possess a good accuracy. the $eno$-like scheme corresponding to $k = 3$ can ge the precision as good as van leer-type schemes, and is numerically stable. moreover, the $eno$-like schemes for larger k may suffer from oscillations.