# American Institute of Mathematical Sciences

August  2016, 36(8): 4383-4402. doi: 10.3934/dcds.2016.36.4383

## Mesh convergence for turbulent combustion

 1 Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, United States, United States, United States, United States 2 Department of Computer Science, ETH Zurich, Switzerland 3 Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, United States

Received  June 2015 Revised  October 2015 Published  March 2016

Our central result is a methodology for predicting mesh convergence for three dimensional (3D) turbulent combustion simulations, based on less expensive one dimensional (1D) and two dimensional (2D) simulations. We verify the prediction by comparison to a 3D finite rate chemistry simulation based on a reduced reaction mechanism, and we further verify it by comparison to a completely independent simulation of the same problem. We validate our simulation by comparison to experiment. Additionally, we assess grid requirements for finite rate chemistry with more detailed chemical reaction mechanism. In both cases, the test problem is an engineering scale study of a model scramjet combustor designed by Gamba et al. We find that the mesh requirements are not feasible for finite rate chemistry simulations of engineering scale problems with detailed reaction mechanism, as expected, but these criteria are less severe than the Kolmogorov scale.
Citation: Xiaoxue Gong, Ying Xu, Vinay Mahadeo, Tulin Kaman, Johan Larsson, James Glimm. Mesh convergence for turbulent combustion. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4383-4402. doi: 10.3934/dcds.2016.36.4383
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