What is the potential of high-order methods for predicting turbulent combustion at highly turbulentconditions?

High-order methods have shown potential for improved predictions of aerodynamic flows. It is therefore expected that these advantages are translatable to the application of reacting flows at highly turbulent conditions. This talk examines the potential and reseach needs of high-order methods for predicting such flows. Of particular interest is the discontinuous Galerkin (DG) method. After discussing benefits of DG-methods for application to turbulent combustion, we will examine recent algorithmic developments to enable high-order predictions, which include solution stabilization, flux-discretization, and the treatment of reaction chemistry and complex transport. We will then proceed by reviewing progress on the development of combustion models and subfilter-scale closures that are consistent with the high-order variational formulation. Recent developments of regularized deconvolution methods and variational multiscale methods are discussed as promissing strategies for subfilter terms, and potential benefits of solution adaptation and enrichment are illustrated. Results of turbulent combustion simulations and benchmark calculations against low-order methods are presented. We close by highlighting further opportunities of high-order methods for application to combustion problems at highly turbulent conditions.