An unstructured high-order finite-volume scheme for the simulation of reactive multi-species flows

In this work, a high-order finite-volume method is combined with an iterative projection approach to solve transport equations for reactive fluids in the low-Mach number regime. The proposed solution algorithm is fully collocated in both space and time and employs a vertex-centered -exact discretization to achieve truly third-order spatial accuracy, even on fully unstructured median-dual grids. To enhance both accuracy and robustness, viscous and convective fluxes are treated consistently within the high-order framework. Convective fluxes are discretized using a central face-value approximation augmented with adaptive numerical dissipation control, governed by a novel gradient-limiting strategy that selectively reduces the order of accuracy near strong gradients while minimizing artificial dissipation elsewhere. The performance of the method is assessed against a conventional finite-volume scheme for unstructured grids, with a focus on reducing the number of computational elements required for accurate simulations. Benchmark test cases include the isochoric advection of a hydrogen-oxygen mixture, convection of a pseudo-isentropic vortex, and flame kernel–vortex interaction. As a key extension, a large-eddy simulation of a turbulent hydrogen-nitrogen-air diffusion flame on a fully unstructured three-dimensional grid is presented, demonstrating the method’s capability to handle complex variable-density reactive flows in practical combustion scenarios. Results show that the k-exact scheme achieves accurate predictions even on relatively coarse grids, substantially reducing computational cost while maintaining physical fidelity - underscoring its potential for reactive flow simulations in both industrial and research applications.