Large eddy simulation in generalized curvilinear coordinates using conventional approach: Theory and validation

Abstract

SUMMARYLarge eddy simulation (LES) methodology in curvilinear coordinates is presented in this study, where filtering is performed prior to the transformation in contrast to the alternate approach proposed by Jordan [J. Comput. Phys. 1999; 148:322–340], where filtering is done after the transformation. The main objective of the present study is to elaborate on the problems mentioned by Jordan with the conventional approach, and its consequences for the overall accuracy. The paper also provides remedies to the problems associated with the conventional approach. The present method treats the Leonard term in physical space rather than in computational space. Some practical difficulties associated with the alternate approach are also considered. Main advantages with the present conventional approach are: first an existing Reynolds averaged Navier–Stokes code can easily be extended for LES and second a wide range of existing advanced subgrid stress model can be used without any modifications. Filtering in physical space introduces a commutation error between filtering and differentiation due to non‐uniform meshes. The commutation filters in generalized coordinates are presented. LESs of four standard test cases are carried out to validate the present methodology. The four standard test cases are: (i) a lid‐driven cavity at Reynolds number (Re) of 12 000, (ii) a pipe flow at a friction Reynolds number Reτ of 360, (iii) a backward facing step at Re = 5100, and (iv) an axisymmetric confined dump combustor at Re = 11000. The results are validated against the reference data (direct numerical simulation or experiments). The mean velocity profiles and the turbulence intensities compared satisfactorily with the reference data. Copyright © 2011 John Wiley & Sons, Ltd.