Advancements in modern hardware and numerical methods have significantly enhanced the feasibility of scale-resolving simulations, such as direct numerical simulation, for industrial applications. For effective application, these simulations require the generation of realistic incoming turbulence to ensure accurate predictions of the flow field. The challenge of introducing realistic turbulence in the computational domain is addressed in Nektar++ by the source-term formulation of the Synthetic Eddy Method (SEM). The source-term formulation of this method has been developed for the incompressible and compressible solvers. Here, the source formulation of the SEM is applied to a compressible plane turbulent channel flow.

Figure 1(a) shows a schematic diagram of a plane channel flow and synthetic eddy region. The synthetic eddy region is where the eddies are injected into the domain by adding a source-term to the conservation equation to drive the solution to the desired turbulent field. Since the SEM implemented here is based on the source-term formulation, the synthetic region is placed, in this case, slightly downstream of the inlet boundary condition. The synthetic region does not need to extend throughout the entire domain in the y– and z-directions, it can be strategically located in the region of interest. In the first time step, all the eddies are injected in random positions into the synthetic region. Looking at the movement of a single eddy in the synthetic region as illustrated in figure 1(b). After its injection, the eddy moves downstream generating fluctuations in the flow field. When the eddy leaves through the outlet plane of the synthetic region, another eddy is randomly re-injected in the inlet plane.

Looking at the flow field, figure 2 illustrates the isosurfaces of the Q-criterion for the compressible channel flow. We observe that slightly downstream of the inflow boundary, eddies are injected into the flow field at the inlet plane of the synthetic eddy region. The elongated structures observed near the wall are convected downstream by the mean flow and eventually evolve into classical hairpin vortex structures, which become more pronounced near the center of the channel. Thus, the compressible synthetic turbulence generator is capable of producing realistic flow fields.