This software computes a single-phase turbulent flow. The solution is independent of the grid spacing on which it is computed, and on the discretization order used for the differential equations. Grid spacing and discretization-order independence can be achieved by reformulating the large-eddy simulation (LES) equations. Previous software followed the conventional LES equations, whereas the present one follows the explicitly filtered formulation (EFLES).

In LES, it is often assumed that the filter width is equal to 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 that 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 modeling and numerical choices. Grid-spacing-independent LES predictions unaffected by numerical choices are necessary to validate LES models through comparison with a trusted template.

Such a template was created through Direct Numerical Simulation (DNS). Then, simulations were conducted using the conventional LES equations, and also LES equations that were 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 (EFLES). LES was conducted with four SGS models and then, EFLES is performed with two of the SGS models used in LES; the results from all these simulations were 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 follows 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, were analyzed.

This work was done by Josette Bellan of Caltech and Senthilkumaran Radhakrishnan for NASA’s Jet Propulsion Laboratory. For more information, contact This email address is being protected from spambots. You need JavaScript enabled to view it..

The software used in this innovation is available for commercial licensing. Please contact Dan Broderick at This email address is being protected from spambots. You need JavaScript enabled to view it.. Refer to NPO-49208.


NASA Tech Briefs Magazine

This article first appeared in the February, 2015 issue of NASA Tech Briefs Magazine.

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