m_adm Module

Actuator Disc Model (ADM) turbine forcing (iturbine = 2).

Each turbine is a disc that applies a thrust force computed from a thrust coefficient and the disc-averaged inflow velocity. The force is regularised and projected onto the Eulerian grid with a per-disc kernel $\gamma$, built once at init and normalised to sum to one. This operation is also commonly called force spreading or smearing.

The kernels of all discs share two fields, so device memory does not grow with the number of discs: gamma holds the kernel values and disc_id labels each grid point with the disc whose kernel is largest there (zero where every kernel vanishes). Kernels of separate discs must therefore not overlap; init stops if a significant part of any kernel lies where another disc's kernel is larger. The disc-averaged velocities of all discs come from one labelled weighted sum and one MPI reduction, and the projected forces of all discs are added to the momentum RHS in one labelled axpy.

For yaw angle $\psi$ and tilt angle $\theta$, the rotor-normal vector used by the model is $$\mathbf{n} = \left(\cos\psi\cos\theta,\ \sin\theta,\ -\sin\psi\right).$$ For a grid point $\mathbf{x}$ and disc centre $\mathbf{x}_c$, the normal and radial distances are $$\delta_N = (\mathbf{x}-\mathbf{x}_c)\cdot\mathbf{n}, \qquad \delta_R = \left\lVert (\mathbf{x}-\mathbf{x}_c)-\delta_N\mathbf{n} \right\rVert_2.$$ The unnormalised anisotropic regularisation kernel is Gaussian in the disc-normal direction and eighth-order super-Gaussian in the radial direction: $$\widetilde{\gamma}(\mathbf{x}) = \exp\left[ -\left( \frac{\delta_N^2}{(h/2)^2} + \frac{\delta_R^8}{(D/2)^8} \right) \right], \qquad h = \max\left(\frac{D}{8},\,1.5\Delta_n\right),$$ where $$\Delta_n = \sqrt{(\Delta x\,n_x)^2+(\Delta y\,n_y)^2+(\Delta z\,n_z)^2}.$$ The discrete kernel is normalised globally over all MPI ranks: $$\gamma_i = \frac{\widetilde{\gamma}_i} {\sum_j\widetilde{\gamma}_j}, \qquad \sum_i\gamma_i=1.$$ Consequently, the instantaneous disc-normal velocity is the weighted global average $$U_d = \sum_i \gamma_i\,\mathbf{u}_i\cdot\mathbf{n}.$$ an optional first-order low-pass filter is applied: $$\beta = \frac{\Delta t/T_{\mathrm{relax}}} {1+\Delta t/T_{\mathrm{relax}}}, \qquad U_F^{n} = \beta U_d^{n} + (1-\beta)U_F^{n-1}.$$ On the first update, or when $T_{\mathrm{relax}}<0$, $U_F=U_d$. The local thrust coefficient, thrust, and power are $$C_T' = \frac{C_T}{(1-\alpha)^2}, \qquad T = \frac{1}{2}\rho C_T' A U_F^2, \qquad P = T U_F, \qquad A = \frac{\pi D^2}{4}.$$ Finally, the acceleration added to the momentum right-hand side at grid point $i$ is $$\mathbf{f}_i = -\frac{T}{\rho\,\Delta V}\,\gamma_i\,\mathbf{n}.$$