Numerical Solutions to Compressible Flows in a Nozzle with Variable Cross-section

Compressible flows in a nozzle can be modeled by the gas dynamics equations in one-dimensional space with source terms. It turns out that along stationary waves, the entropy is conserved. Investigating properties of the system leads us to the determination of stationary waves. Relying on this analysis, we construct a numerical scheme which takes into account the use of stationary waves. Our scheme is shown to be capable of maintaining equilibrium states. This demonstrates the efficiency of the new scheme over classical ones, which usually give unsatisfactory results when reducing the refinement of the mesh-size. Moreover, our scheme converges much faster than the classical ones in most cases.