Localized artificial diffusivity scheme for deflagrations and detonation waves

The ability of a localized artificial diffusivity (LAD) method to capture reactive flow discontinuities, such as deflagrations and detonations, using high-order compact differencing scheme is evaluated in this paper. Different types of steady and unsteady problems under 1D and 2D conditions are tested. For the laminar premixed flame, the flame speed and numerical flame thickness are used when evaluating the accuracy of the LAD results. As the grid spacing increases, the physical behaviour of the flame is maintained using LAD. It is shown that the ability to obtain accurate flame structure are controlled by the artificial diffusivity terms for both the thermal conductivity and species diffusivity. The artificial species diffusivity term is found to affect the L2 error of the solution when the mesh is progressively refined. However, the error reduces according to the order of the discretization error for the schemes being used when the LAD terms are switched off. The choice of the model constants for the LAD terms, selected previously for non-reacting cases, are found appropriate as the flame thickness and chemical reaction rate are found to adjust such that the flame speed is well predicted. The finding is verified further using a 2D configuration involving vortex-flame interaction. The ability of LAD to retain the flame properties allows for the flame response to vortex interaction to be captured at larger grid sizes. For the CJ detonation wave, the structure of the detonation wave is well captured without spurious oscillations. The amplitude of wiggles near a shock or contact discontinuity and the number of grid points used to capture the discontinuity are largely independent of the mesh size. A 2D CJ detonation configuration is also investigated and shows the ability of the LAD method to capture the transverse variations of the detonation wave when subjected to an initial perturbation. The study demonstrates that the LAD method does not show any major detrimental effect on the discontinuity capturing under the conditions examined for both deflagration and detonation wave.