Efficient implementation of complex equations of state in a high-order framework

In the last decades, the interest in non-ideal compressible fluid dynamics (NICFD) flows and high-order accurate numerical methods, such as discontinuous Galerkin (dG), has quickly grown. In fact, advanced simulation capabilities are of paramount importance to develop new sustainable technologies with higher efficiency and low environmental impact, and to decrease the use of expensive experimental facilities. Nowadays however, the coupling of accurate Computational Fluid Dynamics (CFD) solvers with sophisticated thermodynamic models has been investigated mainly in the finite volume (FV) framework. Moreover, the solution of complex equations of state (EoS) has a too high computational cost for real-life use in industry, which is often overcome with the look-up table (LuT) interpolation approach. LuTs seem to be more suitable for FV solvers rather than high-order or finite element ones, since the interpolation error introduced may deteriorate the higher accuracy provided by these numerical methods. The novelty of this work lies in the assessment of an efficient implementation for real gas simulations in a high-order solver, by resorting to structured LuTs and automatic differentiation (AD). The proposed implementation is assessed with the computation of the inviscid and turbulent flow around a NACA0012. This approach guarantees an overhead of the computational cost around 17% with respect to an ideal gas solver with manually derived jacobian matrix.