High-order numerical scheme for compressible multi-component real gas flows using an extension of the Roe approximate Riemann solver and specific Monotonicity-Preserving constraints

The purpose of this paper is to develop a high-order shock-capturing scheme capable predicting flows where shock waves with high-temperature jumps interact multi-component real gas mixtures, assuming local thermodynamic equilibrium. We first propose generalization the Roe solver for distinct species non-ideal properties that relies on original method proposed by Vinokur & Montagné [1]. This uses an approximation compressibility factors estimate coherent value speed sound at averaged state. state introduced in One-Step Monotonicity-Preserving (OSMP) scheme, originally developed Daru and Tenaud [2], obtain extension Lax-Wendroff procedure adequate dealing flows. To avoid inconsistencies evolution average over large stencil, we reformulate discrete total energy flux initial solver. new formulation combination Riemann invariants related mass fractions avoids influence independent values computation. An additional M-P constraint allows discontinuities. Based estimated our method, demonstrate equivalent selecting completely fulfill jump relationships problem. properly capture discontinuities while optimizing number numerical cells, OSMP combined Adaptive Multiresolution [3] automatically refine grid regions steep gradients occur coarsen elsewhere. order evaluated convection density fraction waves. Its capability capturing validated 1-D tube problem mixture Nitrogen, Oxygen dense refrigerant R22 gases. show smooth solutions, as well discontinuities, are recovered high accuracy. 2-D interaction between wave Air cylindrical bubble initially filled also considered. Present results compare very both recent fully resolved solution ideal gases experimental obtained Compared solutions corresponding calorically perfect gas, drastic changes recorded predicted temperature flow patterns justify use relevant thermodynamics account properties.