Numerical Dissipation Rate Analysis of Finite-Volume and Continuous-Galerkin Methods for LES of Combustor Flow-Field

A growing body of literature indicates that element-based high-order methods can exhibit considerable accuracy/cost benefit over conventional second-order finite-volume (FV) methods for large-eddy simulations (LES). This may even hold true for complex configurations relevant to industry that involve under-resolving unstructured grids. However, it is not often clear whether the accuracy/cost benefit stems from the low-dissipative nature of the high-order numerical schemes or from using a different LES approach (implicit/explicit), or a combination of the two. The present paper employs a numerical dissipation rate analysis technique due to Schranner et al. (Comput Fluids 114:84–97, 2015) to better understand the reasons for the high-order benefit seen previously on a complex LES test case related to gas-turbine combustors. It is established that a high(fifth)-order LES run provides better accuracy than its second-order FV counterpart at the same computational cost primarily because of lower numerical dissipation and the LES model dissipation has a secondary role to play. The numerical dissipation is found to contribute 60–90% of the total (numerical and LES model) dissipation.