Extension and Assessment of the Rotated-RoeM Scheme for Hypersonic Equilibrium Flow Computation

초록

This paper presents the extension of the Rotated-RoeM flux scheme to hypersonic equilibrium flow computations. Originally designed for ideal gases, the compact stencil of the scheme efficiently resolves strong shock waves. Incorporating a rotated-hybrid approach suppressed spurious oscillations along the grid-aligned shocks, ensuring numerical stability. A Mach-number-based weighting function enhanced accuracy by distinguishing between boundary layer flows and shock instabilities. A key feature of the Rotated-RoeM scheme is its ability to preserve total enthalpy, which not only contributes to energy conservation but also enables the extension of the scheme to accommodate a general equation of state (EOS). Applying a general EOS in Roe-type schemes typically requires careful treatment of thermodynamic derivatives due to their impact on the eigensystem. However, the Rotated-RoeM scheme simplifies implementation by avoiding the need for partial derivatives, achieved through a modified energy eigenvector that remains independent of these derivatives. The scheme integrating an equilibrium air model was calculated using the IDEA library, a neural network-based collection of air property models, to address the aerodynamic heating effects in hypersonic atmospheric re-entry. This allowed for efficient and accurate determinations of thermodynamic and transport properties under equilibrium conditions. Extensive numerical simulations validated the capability of the Rotated-RoeM scheme in resolving multi-dimensional strong shock waves, capturing the heat transfer boundary layers, and predicting the convective heat flux near the stagnation region of equilibrium flow. This scheme maintained accuracy and stability in resolving hypersonic equilibrium flow as in ideal gas flow.