An Explicit Filtering Method for Large Eddy Simulation on Unstructured Meshes

Abstract

This paper presents the development of an explicit filtering method for Large Eddy simulation in the framework of unstructured grids. The proposed method relies on the approximate deconvolution model, complemented with a modified Smagorinsky term. This term aims at accountin g for long-range interactions in the wavenumber space between resolved and subgrid scales. Both a classical and a multiscale formulation of this term are considered. An analytical evaluation procedure is described in order to adjust the model coefficient to our explicit filtering framework. The method relies on the introduction o f a discrete filtering operator. For that purpose, a simple volume averaging operator has been chosen in order to perform explicit filtering because of its ease of implementation on unstructured meshes. A discrete characterization procedure of this operator is also proposed in order to estimate locally in space the shape of the filter wh ich is required for the analytical evaluation of the Smagorinsky coefficient. The method is assessed using both h exahedral and tetrahedral grids on a classical homogneneous isotropic turbulence test case. First results obtained for the turbulent flow around a circular cylinder, at a diameter-based Reynolds number of 3,900 are also presented. I. Introduction Large eddy simulation is a tridimensional method that allows a fine unsteady analysis of turbulent flows. This method is based on a separation between large and small scales of the flow, only large scales being resolved while the small one’s influence is represented by a subgrid scale model. This separ ation between large and small scales is generally assumed in practice as being due to a high-pass spatial filtering of th e solution. Unfortunately, on unstructured meshes, many parameters prevent from exactly characterizing the effect ive filtering operator and therefore to develop adapted subg rid models to account for the unresolved scales. Besides, it sho uld be necessary to account for the numerical scheme’s influence, which can act as an additionnal filtering step 1 . Indeed, the use of dissipative numerical scheme to perform large eddy simulations on unstructured meshes is not well suitable because of their interaction with the subgrid scale model. Therefore, the use of more accurate numerical schemes seems fundamentally more suitable. However, the development of high-order schemes on unstructured meshes remains a significant challenge today and such schemes are moreover generally observed to be unstable in realistic configuratio ns, thus requiring an additional artificial stabilization. In this study, we will investigate a possible alternative to perform LES on unstructured grids, which relies on the use of explicit filtering methods. In such methods, a discrete fil tering operator is applied explicitely during the simulati on. In this specific context, the effective filter then becomes dire ctly known and is no longer assumed to be due implicitely to the grid and to the numerical scheme. Indeed, the introduction of this explicit filter allows to control the effective filt er. This technique seems also very interesting by its potential stabilizing effects that could make the use of low dissipative numerical schemes possible. In this paper, different strategies for explicit filtering w ill be discussed and an approximate deconvolution method based on Stolz and Adams 2 original approach will be presented. Subgrid scale modelin g associated to this method will also be considered. Since this approach is based on the intro duction of a specific discrete filter, a method to construct a discrete filtering operator on unstructured meshes will the refore be proposed. The explicit filtering method will first be detailed in sectio n II, where two possible implementations of the Approximate Deconvolution Method (ADM) will be considered. Since ADM only makes it possible to account for local interactions in the wavenumber space, an additional closure based on the Smagorinsky model will be proposed in order to