Hello Thibaut,
Thank you for the very good and technically relevant questions,
Your interpretation is generally correct: the aerodynamic forces are indeed obtained from the pressure and wall shear stress distributions integrated over the model surface. However, the residuals shown in CFD solvers (including RWIND/OpenFOAM-based workflows) do not necessarily represent the same mathematical quantity, which is why their convergence behavior can differ significantly.
Here is a more detailed explanation.
1. What does the residual F represent?
In RWIND, the quantities:
are not primary equation residuals like the pressure residual p.
They are instead monitoring quantities derived from the flow solution during the iterations.
In practice:
-
Fx, Fy, Fz represent the evolution of the integrated aerodynamic forces acting on the model in each Cartesian direction.
-
F is typically the resultant (magnitude) of the aerodynamic force vector:
So the plotted “force residuals” are usually related to the iteration-to-iteration variation of these integrated forces rather than the algebraic residual of a discretized transport equation. This is an important distinction.
2. How are Fx, Fy, and Fz computed?
The aerodynamic forces are computed by integrating:
over the model surface.
In continuous form:
where:
The directional components are then:
Numerically, RWIND/OpenFOAM evaluates these quantities after every iteration from the current flow field solution.
3. Why can force residuals behave very differently from pressure residuals?
This is actually very common in CFD. The key reason is that:
The pressure residual measures the local algebraic convergence of the pressure equation, while force monitors are global integral quantities.
These are fundamentally different metrics.
Pressure residual (p)
The pressure residual represents how well the discretized pressure equation is satisfied between successive iterations.
It is sensitive to:
It is therefore a field equation convergence metric.
Force monitors (Fx, Fy, Fz)
The forces are surface-integrated quantities.
Because of the integration:
-
local pressure oscillations may cancel out,
-
errors in different regions may compensate each other,
-
small local non-converged regions may have negligible effect on total force.
Therefore, it is completely possible that:
The opposite can also happen:
-
pressure residuals appear low,
-
but forces still oscillate due to vortex shedding, separation instability, or insufficient physical convergence.
4. Why are your force residuals oscillating?
From your graph, the behavior suggests:
-
The pressure residual decreases relatively smoothly,
-
while especially one force component (likely Fy) shows strong oscillations.
This usually indicates one of the following:
A) Physical unsteadiness in the flow
For separated bluff-body flows:
-
vortex shedding,
-
wake instability,
-
shear layer oscillation
can produce fluctuating integrated forces even in nominally “steady” RANS calculations.
This is very common around:
-
sharp corners,
-
roof edges,
-
cylinders,
-
curved roofs,
-
membrane structures.
B) Sensitivity of integrated forces
The total force may be highly sensitive to:
-
separation point movement,
-
local recirculation zones,
-
wake asymmetry.
A tiny change in separation can strongly modify integrated lift/side force while pressure residuals remain relatively small.
C) Numerical reasons
Force monitors are also more sensitive to:
-
mesh refinement near separation zones,
-
wall treatment,
-
y+ distribution,
-
turbulence model behavior,
-
relaxation factors.
5. Should force convergence be considered more important than pressure convergence?
For engineering CFD, usually:
The convergence of engineering target quantities is more important than residuals alone.
So if your objective is:
-
global wind loads,
-
drag coefficients,
-
base reactions,
-
structural loading,
then stabilization of:
is often more important than achieving an extremely low pressure residual.
However, this does not mean residuals are irrelevant.
A good engineering CFD solution normally requires BOTH:
Numerical convergence
Residuals sufficiently reduced.
Typical practical ranges for steady RANS:
-
(10^{-3}) → acceptable engineering level,
-
(10^{-4}) or lower → preferable,
-
Lower may be needed for sensitive flows.
Physical convergence
Monitored quantities become statistically stable:
-
forces,
-
moments,
-
pressure coefficients,
-
velocity probes.
6. Which criterion is usually more meaningful in practice?
For wind engineering applications:
| Quantity |
Importance |
| Pressure residual |
Numerical convergence indicator |
| Velocity residuals |
Flow-field stabilization |
| Fx/Fy/Fz stabilization |
Engineering load convergence |
| Cp stabilization |
Local pressure reliability |
For structural wind engineering, many engineers actually trust:
more than residual values alone.
7. Important practical remark for RWIND / steady RANS
For strongly separated aerodynamic flows, a perfectly monotonic residual decay is often unrealistic. Especially for:
-
sharp-edged buildings,
-
canopies,
-
tensile membranes,
-
free-form roofs,
-
stadiums,
small oscillations in force monitors are expected.
Therefore, the key question is usually:
Are the monitored engineering quantities fluctuating around a statistically stable mean?
rather than:
Did every residual reach an arbitrarily low value?
8. Recommended validation workflow
For engineering validation, I would recommend:
Step 1 — Residual monitoring
Ensure residuals decrease sufficiently:
Step 2 — Monitor forces
Check whether:
reach stable mean values.
Step 3 — Mesh sensitivity study
Compare:
-
global forces,
-
Cp distributions,
-
separation regions
across multiple meshes.
This is often more important than residual magnitude alone.
Step 4 — Compare with references
If possible:
Please let me know if you have more questions,
Best regards,
Mahyar Kazemian
