AeroSim Docs
Skin friction (IBM)¶
Wall skin friction is the quantity that separates a drag estimate into its viscous and pressure parts and sets the near-wall mesh requirement through \(y^{+}\). Nassu samples it directly on every immersed body from the resolved stress, reusing the IBM combine interpolation, so the friction reported on a body does not depend on the boundary condition that body actually runs - a plain no-slip IBM body with no wall model reports a friction just the same.
The wall shear stress¶
The primitive quantity is the wall shear stress, the tangential viscous traction the fluid exerts on the surface. For a wall whose outward normal is \(\mathbf{n}\) and whose local tangential flow direction is \(\mathbf{t}\), it is set by the wall-normal gradient of the tangential velocity:
where \(\mu = \rho\nu\) is the dynamic viscosity and \(S_{nt}\) is the wall-normal-tangential component of the rate-of-strain tensor at the wall. The second form is exact in incompressible flow and is the one the lattice Boltzmann method recovers naturally, because \(S_{\alpha\beta}\) is carried by the non-equilibrium part of the populations rather than reconstructed from velocity differences (Krüger et al.[1]).
From \(\tau_{\mathrm{w}}\) follow the quantities reported per body:
the skin-friction coefficient \(C_{f}\), the friction velocity \(u_{\tau}\), and the wall-unit distance \(y^{+}\) of the first sampled point.
How Nassu measures it¶
At the export frequency a read-only friction-sampling pass runs for every immersed body. It is independent of the body’s boundary condition: a body running plain no-slip IBM, a wall-modeled body, and a moving body all report friction computed the same way, so a single field is comparable across the whole domain.
The pass reuses the IBM machinery already in place. Along each Lagrangian node’s outward normal it samples the fluid at the wall-model reference distance with the same Euler-to-Lagrange combine interpolation used to build the immersed-boundary forcing (see Combine and Spread). It spreads no force back to the fluid, so it never perturbs the solution.
Viscous traction from the resolved stress¶
Everything is built from the viscous traction vector, formed from the interpolated rate-of-strain \(S_{\alpha\beta}\), which the lattice Boltzmann method carries in the non-equilibrium part of the populations and Nassu stores at every node (and corrects for the IBM body force):
The total viscosity carries the subgrid contribution \(\nu_{\mathrm{SGS}}\) from the Smagorinsky model, so the traction reflects the modeled stress wherever the LES adds eddy viscosity near the wall (with LES off, \(\nu_{\mathrm{total}} = \nu_{0}\)).
Friction velocity from the wall shear stress¶
The wall shear stress \(\tau_{\mathrm{w}}\) is the magnitude of the tangential part of the traction, splitting it against the wall normal \(n_{\alpha}\) at each sampled point:
and the \(C_{f}\), \(u_{\mathrm{friction}}\) and \(y^{+}\) of (2) follow from it directly. Because the wall shear comes entirely from the resolved stress, the friction velocity and \(y^{+}\) are defined for any body - a plain no-slip IBM body with no wall model, a wall-modeled body, or a moving body - with no dependence whatsoever on the body’s boundary condition. This is the figure reported per node.
Aggregation onto the source geometry¶
The runtime IBM node set subdivides each source triangle, so it can hold millions of Lagrangian nodes that do not map one-to-one onto the geometry’s faces. Reporting per-node would be unwieldy and tied to a resolution-dependent mesh. The pass therefore aggregates the per-node traction back onto the source-geometry triangles by an area-weighted mean, collapsing the runtime nodes (order \(10^{6}\)) onto the original faces (order \(10^{4}\)) while preserving the integral.
On the host the aggregated traction at each triangle is split against the exact triangle normal into a normal and a tangential part:
The tangential part is the skin-friction stress, giving the local \(C_{f}\) from (2). The normal part is the viscous normal traction, not the mechanical pressure: the exported traction is purely viscous (\(2\rho\nu\,\mathbf{S}\cdot\mathbf{n}\)) and carries no \(\rho c_{s}^{2}\) pressure term. The reader therefore labels its body-integrated coefficients Cd_normal_viscous and Cd_friction, and Cd_total is the body’s total viscous force.
For a bluff body the dominant form drag is the surface-pressure contribution. The same friction pass samples the wall pressure at the reference point (co-located with the reference velocity), through the equation of state \(p = \rho\,(1 + \theta)\,c_{s}^{2}\), and stores it per node as pressure. The \(\theta\) (temperature-deviation) term folds in the fluid temperature when it carries one and is \(0\) for isothermal flow (\(p = \rho\,c_{s}^{2}\)). The host builds the surface pressure coefficient \(C_{p} = (p - p_{\text{ref}}) / (\tfrac{1}{2}\rho_{\text{ref}} U_{\text{ref}}^{2})\) and integrates \(-C_{p}\,\mathbf{n}\) over the body for the form-drag coefficient. Because drag projects linearly onto the flow direction, the full bluff-body drag is the exact sum \(C_{d} = C_{d,\text{pressure}} + C_{d,\text{viscous}}\).
Validity¶
The traction comes from the resolved and interpolated stress, so its fidelity tracks the near-wall resolution: at a well-resolved wall it is the viscous stress directly, while at a marginally-resolved wall the subgrid viscosity \(\nu_{\mathrm{SGS}}\) carries part of the shear and the reported traction includes that modeled contribution. The friction velocity follows the equilibrium thin-boundary-layer closure, which is exact for an attached equilibrium boundary layer and degrades gracefully where the wall-model assumptions weaken (see the wall-model limits). Local \(C_{f}\) is an instantaneous, per-triangle quantity and benefits from time averaging; for bodies of revolution, azimuthal averaging further smooths the distribution and sharpens the comparison against reference data.