Accurate heat flux predictions require extremely small first cell spacing

[Hanquist]

We have used SU2 and SU2-NEMO to predict the heat flux for various shapes in a high-speed flow. Something we have observed is that SU2 requires an extremely small first cell spacing to get an accurate and grid-independent prediction for heat flux. For example, this first cell space is often 1E-9 to 1E-10 m with SU2; whereas with other codes it is a micrometer. The latter is in line with the general rule of thumb of setting the first cell height so that the first cell Reynold's number is between 0.1 and 1.0.

Discussing with @jtneedels and @WallyMaier, we think it may have to do with how the temperature gradient is calculated in CNSSolver.cpp:

/--- Compute the normal gradient in temperature using Twall ---/

su2double dTdn = -(There - Twall)/dist_ij;

/--- Apply a weak boundary condition for the energy equation.
Compute the residual due to the prescribed heat flux. ---/

su2double Res_Conv = 0.0; su2double Res_Visc = thermal_conductivity * dTdn * Area;

which may result in a first-order approximation for the temperature gradient causing this requirement for an extremely small cell size to recover the true gradient. I would be interested to see if calculating this gradient similar to CFVMFlowSolverBase.ini. For example,
for (iDim = 0; iDim < nDim; iDim++) { Grad_Temp[iDim] = nodes->GetGradient_Primitive(iPoint, prim_idx.Temperature(), iDim); }

su2double dTdn = -GeometryToolbox::DotProduct(nDim, Grad_Temp, UnitNormal);

I tried checking this but quickly found out, I am not familiar enough with the code structure to implement.

[pcarruscag]

It's been discussed in other places that the problem is probably the inconsistency between what is done in the boundary condition vs what is done for post processing (using delta T vs using the gradient). Gradients are first order at best.
So even for heat flux walls it takes a lot of refinement to see agreement.
You cannot just use the gradient in the boundary condition otherwise you don't have a way of bringing in Twall. But you can make the post processing consistent with the boundary condition (use delta T instead of the gradient).

[pcarruscag]

@Hanquist can you give this another try with non-nemo cases to see if #2394 helped?