Advances in large eddy simulation methodology for complex flows Parviz Moin Center for Turbulence Research, Stanford University and NASA-Ames, USA Abstract A review is provided of the recent advances in the derivation of the constitutive equations for large eddy simulation, subgrid scale modeling, wall modeling and applications of LES to turbulent combustion. The majority of the paper focuses on a review of two numerical methods for LES in complex geometry: the immersed boundary method and an unstructured mesh scheme. The latter scheme is applied to LES of a sector of a combustor of an operational gas turbine engine. Ó 2002 Published by Elsevier Science Inc. 1. Introduction The advent of massively parallel computers and af- fordable workstation clusters has stimulated industry interest in applying LES to engineering flows. Resolu- tion of large turbulent eddies is required in many ap- plications such as those involving turbulent mixing and aerodynamic noise. Most of these applications require computation of turbulence in complex geometries. Un- fortunately, in most cases, numerical methods used for efficient RANS computations are not appropriate for LES. In contrast to RANS where the steady or unsteady solutions are smooth, turbulent flows have broad band spectra, and most numerical methods used for robust RANS computations are inaccurate in the representa- tion of the medium to small resolved eddies in LES. For example, the use of upwind schemes is prevalent in in- dustrial CFD and it has been demonstrated that the inherent numerical dissipation of even the high order upwind schemes can lead to excessive dissipation of the resolved turbulent structures (Mittal and Moin, 1997). If the purpose of using LES is to capture the turbulence structures, which are not available from RANS, then the numerical methods used in LES should be sufficiently accurate in representing their dynamics, rather than re- move them by artificial dissipation. Application of LES to industrial problems requires good subgrid scale models, fast computers, accurate and robust numerical methods suitable for complex config- urations and reliable experimental data for validation. Of these required ingredients, development of numerical methods has received the least attention. Although sig- nificant advances have been made in subgrid scale model development, the models await to be tested in truly complex heterogeneous turbulent flows, so that the need for improvements and further research can be identified. Fundamental advances in numerical algorithms are needed before this testing can take place and LES can transition to industry. The focus of this review is on the development of numerical methods for LES. In the main body of the paper I describe two nu- merical methods that have been developed at the Center for Turbulence Research for LES in complex domains. Recent major advances in other components of LES are highlighted in this section. One approach is based on the immersed boundary (IB) method where body forces are used to enforce the boundary conditions and hence ac- count for the geometry. In the past typical calculations with the IB method were done on a Cartesian mesh, but recently it has been used effectively in conjunction with curvilinear and unstructured grids. Applications of this method include the flow in an impeller stirred tank, flow around a road vehicle with drag reduction devices and tip clearance flow in a stator/rotor combination. The second numerical method is designed for unstructured grids with arbitrary elements. This is a fully conservative method and is being used for computations in the combustor of a gas turbine jet engine. 1.1. Filtering and constitutive equations With the development of spatial filters that commute with differentiation, the governing LES equations are International Journal of Heat and Fluid Flow 23 (2002) 710–720 www.elsevier.com/locate/ijhff E-mail address: moin@stanford.edu (P. Moin). 0142-727X/02/$ - see front matter Ó 2002 Published by Elsevier Science Inc. PII:S0142-727X(02)00167-4