When beta features are enabled, the Roe flux-difference splitting scheme can be used with the pressure-based solvers for compressible single-phase flow, both steady-state and transient. Compared with the default Rhie-Chow flux method (described in the section on discretization of the continuity equation in the Fluent Theory Guide), the Roe scheme shows much less dissipation in areas of strong pressure and velocity gradients in supersonic flows and produces less smearing of shocks. In can improve feature resolution in such areas at the expense of reduced numerical stability compared with the Rhie-Chow method.
The Roe flux-difference splitting scheme implements upwinding of the inviscid fluxes based on the direction of the characteristics of the flow equations [5]. In the pressure-based solver framework, the matrix form of the preconditioned Roe flux (Equation 19–6) is converted to scalar form with:
 | (19–2) |
The fluxes contain convective and pressure contributions. The
convective part is computed based on the face-normal velocity, 
, and the upwinded flow variables. The pressure part is computed
from the face pressure, 
, projected on the
appropriate coordinate directions. The face-normal velocity and pressure
are expressed as Mach-weighted averages of the adjacent cell values [1]:
 | (19–3) |
where 
,
, 
and 
, 
, 
depend on the preconditioned face Mach number, 
.
In the low-Mach-number limit, 
and the face velocity and pressure reduce
to an approximately arithmetic average of the left and right cell
values, plus dissipation:
 | (19–4) |
For supersonic flow, the face velocity and pressure (Equation 19–3) reduce to pure upwinding:
 | (19–5) |
The reduction to pure upwinding in the case of supersonic flow
is in contrast with the Rhie-Chow method, in which the extra dissipation
terms associated with 
and 
remain [4].
The Roe flux method is available in the pressure-based solver for compressible single-phase flow. It is available for both steady-state and transient simulations using any of the pressure-velocity coupling schemes. Compared with the default Rhie-Chow flux method (described in the section on discretization of the continuity equation in the Fluent Theory Guide), the Roe scheme shows much less dissipation in areas of strong pressure and velocity gradients in supersonic flows and produces less smearing of shocks. In can improve feature resolution in such areas at the expense of reduced numerical stability compared with the Rhie-Chow method.
After enabling beta features (Introduction), the Roe-FDS method is available under Flux Type in the Solution Methods task page (when the Auto Select option is disabled).
Recommendations
As a result of the reduced dissipation of the Roe-FDS flux method, divergence may occur during the solution. The following strategies may help alleviate divergence when using Roe-FDS.
Start the simulation with the Rhie-Chow flux method and switch to the Roe-FDS method.
Start with first order discretization of pressure, velocity, temperature, and density and then switch to higher-order discretization methods.
Reduce the under-relaxation values, in particular for temperature.
For steady-state flows, consider using the coupled solver with global time step selected for the pseudo time method, as this combination has been observed to give better convergence. If divergence is observed with this pseudo time method, try reducing the time scale factor for the energy equation in the Expert tab of the Advanced Solution Controls dialog box. For details on setting solution controls for the pseudo time method, see Performing Calculations with a Pseudo Time Method in the Fluent User's Guide.