Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of compressible single-phase flow

Abstract

AbstractIn large-eddy simulation (LES), it is often assumed that the filter width is equal to the grid spacing. Predictions from such LES are grid-spacing dependent since any subgrid-scale (SGS) model used in the LES equations is dependent on the resolved flow field which itself varies with grid spacing. Moreover, numerical errors affect the flow field, especially the smallest resolved scales. Thus, predictions using this approach are affected by both modelling and numerical choices. However, grid-spacing-independent LES predictions unaffected by numerical choices are necessary to validate LES models through comparison with a trusted template. First, such a template is created here through direct numerical simulation (DNS). Then, simulations are conducted using the conventional LES equations and also LES equations which are here reformulated so that the small-scale-producing nonlinear terms in these equations are explicitly filtered (EF) to remove scales smaller than a fixed filter width; this formulation is called EFLES. First, LES is conducted with four SGS models, then EFLES is performed with two of the SGS models used in LES; the results from all these simulations are compared to those from DNS and from the filtered DNS (FDNS). The conventional LES solution is both grid-spacing and spatial discretization-order dependent, thus showing that both of these numerical aspects affect the flow prediction. The solution from the EFLES equations is grid independent for a high-order spatial discretization on all meshes tested. However, low-order discretizations require a finer mesh to reach grid independence. With an eighth-order discretization, a filter-width to grid-spacing ratio of two is sufficient to reach grid independence, while a filter-width to grid-spacing ratio of four is needed to reach grid independence when a fourth- or a sixth-order discretization is employed. On a grid fine enough to be utilized in a DNS, the EFLES solution exhibits grid independence and does not converge to the DNS solution. The velocity-fluctuation spectra of EFLES follow those of FDNS independent of the grid spacing used, in concert with the original concept of LES. The reasons for the different predictions of conventional LES or EFLES according to the SGS model used, and the different characteristics of the EFLES predictions compared to those from conventional LES are analysed.