Approximate Riemann Solvers for the Soave – Redlich – Kwong Equation of State

Three methods for constructing an approximate Riemann solver for the Soave – Redlich – Kwong real gas model are presented: linearization of nonlinear equations, cubic interpolation, and local approximation of the equation of state by a two-term equation of state. These methods are tested by considering the problem of the decay of a discontinuity in a pipe in an axisymmetric setting for the low-molecular and high-molecular substances, including a region of nonclassical gas behavior. It is demonstrated that the linearization method is reasonable only for the testing problems. The method of approximation by cubic splines is acceptable for complex three-dimensional nonstationary calculations. However, it is found that the bicubic interpolation method does not work well for flows with large pressure drops. The local approximation method is the most economical and universal for practical calculations. It has been used for numerical modeling of real gas flows through a safety valve. The results of calculations for hydrogen and water vapor in a wide range of pressure variation are presented. The method of local approximation of the equation of state allows one to describe all features of gas flows for complex problems.