Comparison of the MUSCL-type schemes for a gas flow calculation in de Laval nozzles

In this paper, MUSCL-type schemes applied for the calculation of a one-dimensional inviscid flow of ideal gas in the JPL nozzle of rocket engine are compared. The comparison was carried out on the basis of determined mass flow coefficient. The calculations were performed using the first-order Godunov scheme, the second-and third-order MUSCL schemes, and the third-order MUSCL-Hancock scheme in a combination with the slope limiters such as MINMOD, Van Albada, Van Leer, and Superbee. The Godunov method, the Roe approximate Riemann solver, and the HLLC Riemann solver were used to calculate the numerical fluxes. The Godunov scheme, which is first order accurate in space, leads to a high error in the mass flow rate (1.4%). The MUSCL schemes, which are second and third order accurate in space, give a low error in the mass flow rate (0.017-0.17%). Both the limiter function and the method of solving the Riemann problem (an exact solution of the Riemann problem, the Roy method, and the HLLC method) affect the accuracy in determination of integral characteristics within the limits of hundredths of a percent.