A non-linear residual distribution scheme for real-gas computations

This paper deals with a high-order accurate Residual Distribution scheme for the numerical solution of dense gas flows on unstructured grids. Dense gas-dynamics studies the flow of gases in the thermodynamic region above the upper saturation curve, close to the liquid-vapor critical point. In such conditions, some fluids may exhibit negative values of the fundamental derivative of gas-dynamics, leading to non-classical gas-dynamic behaviors, such as rarefaction shock waves, mixed shock/fan waves, and shock splitting. Due to the complexity in performing reliable experimental studies for non-classical gas-dynamics, accurate numerical simulations of dense gas flows are of paramount importance. In this work, advantages in using high-order methods are highlighted, in terms of number of degrees of freedom and computational time used, for computing the numerical solution with a greater accuracy compared to lower-order methods, even for shocked flows. Several numerical experiments are also performed to assess the influence of the thermodynamic models on the problem solution.