Development of an efficient shock sensor for high-order multi-species compressible flow solvers on unstructured grids

Abstract

Many fluid flows of engineering interest involve high-density ratios, the formation of shock waves, and the presence of multiple chemical species. In these situations, obtaining accurate results depends on the computational fluid dynamics (CFD) algorithm’s ability to ensure stable and robust time and space discretization of the governing equations, effectively minimizing numerical diffusion.

In this work, we develop and evaluate a low-dissipation, high-order solver for the Navier–Stokes equations applicable to compressible, multi-species flows within the OpenFOAM library. We introduce a new shock sensor specifically designed for high-order discretization methods, which guarantees accuracy up to the fourth order in both space and time when using unstructured grids. Additionally, this approach is compatible with real-gas equations of state.

We evaluated the solver performances on three test cases, each chosen for its relevance to real-world engineering problems: a 1D multi-specie shock tube, a 2D shock tube where Richtmyer–Meshkov instability develops as a consequence of bubble-shock interaction, and, finally, the flow through the complex 3D geometry of a high-pressure fuel injector used in propulsion applications, to investigate its performances on unstructured grids. The results confirm the effectiveness of the proposed sensor in scenarios characterized by field discontinuities, shock waves, high-density ratio, and distorted grids. This means that our solver can accurately simulate complex fluid flows in engineering applications where these conditions are often encountered.

The developed high-order scheme and shock sensor were implemented in an OpenFoam solver called rhoCubic4kFoam.