Spatial differencing schemes control the spatial accuracy of the simulation. Several spatial differencing schemes are available in CFD-ACE+ to estimate the convective term in the transport equations. The Spatial tab under SC (Solver Control) allows the user to select a spatial differencing scheme as shown in Figure 1.

Figure 1. Spatial differencing options in the Solver Control → Spatial tab.

The default scheme is the first-order Upwind Differencing scheme. If higher-order schemes are selected, you can also enter a blending factor to blend the higher-order scheme with the Upwind Differencing scheme for added stability.

Given below is list of spatial differencing schemes available for flow:

• Upwind (1st Order)
• Central (2^nd Order)
• 2^nd Order Upwind or 2^nd Order (2^nd Order)
• 2^nd Order Limiter (2nd Order)
• Van-Leer or 3^rd Order (3^rd Order) [only available for structured meshes]
• Smart Scheme [only available for structured meshes]

Tips for selecting spatial differencing scheme for flow:

1. For steady state problems:
   • Use second order scheme for higher accuracy.
   • If you encounter stability problem with second order, but want a more accurate solution than first order, use second order scheme with non-zero blending factor, for instance 0.5, or you can try using smart scheme where the blending factor is not fixed but dynamically determined according to local flow conditions.
   • Be careful when doing steady state runs on oscillatory flows such as vortex shedding behind an automobile. Convergence with second order will probably be bad, but first order, despite giving a better convergence, is less accurate compared to taking the mean of a partially non-converged second order.
   • A better way for oscillatory flows is transient mode, which is necessary if one is to obtain the Strouhal number of the oscillation. But for a quick averaged solution in steady state mode, you can smooth out the oscillations by coarsening the grid in the wake region, this way second order can give much better convergence and may still be more accurate to first order with finer grid in the wake region.
2. Use second order scheme (central or 2nd order upwind) for simulations having rotating body or rotating boundary for steady state and transient problems.
3. For time-accurate problems like LES, DES, use central scheme or second order upwind.
4. For shock capturing problems, use third order scheme (van-Leer).

If you have any questions about this tip or would like us to discuss some other topic in the future, please let us know.

Regards,
Kartik Shah
ESI CFD Support Team