The Taylor–Green vortex as a benchmark for high-fidelity combustion simulations using low-Mach solvers

Abstract

Verification and validation are crucial steps for the development of any numerical model. While suitable processes have been established for commercial Computational Fluid Dynamics (CFD) codes, more difficult challenges must be faced for high-fidelity solvers. Benchmarks have been proposed in a series of dedicated conferences for non-reacting configurations. However, to our knowledge, no suitable approach has been proposed regarding turbulent reacting flows. The purpose of this article is to present a full verification and validation chain for high-resolution codes employed to simulate turbulent reacting flows, first for Direct Numerical Simulation (DNS) of combustion in the limit of low Mach numbers. The selected configuration builds on top of the Taylor–Green vortex. Verification takes place by comparison with the analytical solution in two dimensions. Validation of the single-component flow is ensured by comparisons with published results obtained with a pseudo-spectral code. Mixing without reaction is then considered, before computing finally a hydrogen-oxygen flame interacting with a 3-D Taylor-Green vortex. Three low-Mach number DNS solvers have been used for this study, demonstrating that the final accuracy of the simulations is of the order of 1% for all quantities considered. All data-sets are publicly available under [1]. The performance of the codes is finally discussed, both in terms of single-node results and regarding parallel efficiency.