### 12.3.1. Spatial Discretization

#### 12.3.1.1. Momentum

SRS models, as described in Scale-Resolving Simulation (SRS) Models – Basic Formulations, serve the main purpose of dissipating the energy out of the turbulence spectrum at the limit of the grid resolution. The eddy viscosity is defined to provide the correct dissipation at the larger LES scales. This assumes that the numerical scheme is non-dissipative and that all dissipation results from the LES model. For this reason, one is required to select a numerical scheme in the LES region with low dissipation, relative to the dissipation provided by a subgrid LES model. Another strategy is to avoid the introduction of the LES (subgrid) eddy viscosity and provide all damping through the numerical scheme. This approach is called MILES (Monotone Integrated Large Eddy Simulation) (Boris et al., 1992 [1]). In ANSYS CFD, the standard LES methodology is followed, whereby the dissipation is introduced by a LES eddy viscosity model and the numerical dissipation is kept at a low value.

In order to achieve low numerical dissipation, you cannot use the standard numerical schemes for convection that were developed for the RANS equations (Second Order Upwind Schemes, or SOU), which are dissipative by nature. In contrast, LES is carried out using Central Difference (CD) schemes. In industrial simulations, second order schemes are typically employed, however, in complex geometries with non-ideal grids, CD methods are frequently unstable and produce unphysical wiggles (see Figure 12.60), which can eventually destroy the solution. To overcome this problem, variations of CD schemes have been developed with more dissipative character, but still much less dissipative than Upwind Schemes. An example is the Bounded Central Difference (BCD) scheme of Jasak et al., 1999 [14].

Figure 12.60: Example of scheme oscillations in T-Junction flow shown by vorticity: (a) CD, (b) BCD

The CD scheme can be used successfully for (WM)LES of simple flows on optimal grids (typically hexahedral grids with low skew) such as channel or pipe flows. For more complex geometries, ELES allows the reduction of the LES domain to a limited region with high quality grids. Under such conditions, CD can be employed inside the LES portion of the grid, while using a standard upwind biased scheme for the RANS part of the domain.

For global models, like SAS or DDES/SDES/SBES, involving RANS and LES portions without a well-defined interface between them, most cases require the use of the BCD scheme, which can also handle both the RANS and LES domains with acceptable accuracy.

When using ELES in ANSYS Fluent, one can also switch the numerical scheme between the RANS and the LES regions (see Cokljat et al., 2009 [2]) by hand.

In ANSYS CFX, the default for the SAS and SBES models is a numerical scheme that switches explicitly between a second order upwind and the CD scheme, based on the state of the flow, using a switch proposed by Strelets, 2001 [33]. This switching scheme is relatively complex and it is advisable to apply the less complex BCD scheme that is also available in the code. In ANSYS CFX there is an additional parameter for the BCD scheme that allows a continuous variation of the scheme from BCD to CD. The parameter is called CDS Bound. CDS Bound=1 applies only to BCD and CDS Bound=0 applies only to CD.

#### 12.3.1.2. Turbulence Equations

The spatial discretization of the convection terms of the turbulence model is not critical in SRS, as the models are dominated by their source terms. The first order upwind scheme is therefore sufficient for these equations, but second order is also suitable.

Note: For SBES, numerical problems have been observed on complex grids with second order turbulence numerics. First order numerics is therefore recommended. Note that this has little effect on the accuracy, because the RANS region is typically insensitive to this switch. In the LES region, the two-equation model is, in any case, overwritten by the selected LES model.

#### 12.3.1.3. Gradients (ANSYS Fluent)

The selection of a specific gradient method is not of much relevance to SRSs on high quality hexahedral meshes. For skewed or polyhedral meshes, the Least Square Method (LSM) is recommended. For the SAS model one should use the LSM or the Green-Gauss Node Based (GGNB). The latter allows a slightly higher sensitivity to initial instabilities.

Release 18.2 - © ANSYS, Inc. All rights reserved.