Conservative upwind difference schemes for compressible flows in a duct

Numerical results are presented, and compared, for four conservative upwind difference schemes for the Euler equations representing the compressible flow of a gas in a duct of variable cross-section. The schemes are applied to a problem involving the interaction and reflection of a converging cylindrical shock. The schemes vary in their treatment of the flux balance, including treating part of it as a source, as well as in the averaging of flow variables, and whether the source term arising out of the geometry of the problem is handled using upwinding or treated as a point source. The schemes are shown to give similar results while being different in construction and implementation, and each having different approximate Jacobians and treatment of the source.