AN EXACT RIEMANN SOLVER FOR HIGH-TEMPERATURE EQUILIBRIUM AIR

An exact solution of one-dimensional Riemann problem for high-temperat ure equilibrium air is presented. Air properties at high temperature a re calculated using a method of equilibrium statistical mechanics. In the expansion region, the Riemann invariants are written in a discrete form by using the Simpson integration method. Shock and expansion equ ations are matched in a system of nonlinear algebraic equations, in wh ich primary variables are reduced to two thermodynamic parameters (pre ssure and temperature); this system is solved by the Newton-Raphson me thod. The shock tube problem is solved for air-air case, which illustr ates the potential use of the present work to analyze an expansion tub e.