Lines Matching refs:phi

325 Denote $\langle \phi \rangle$ as the Reynolds average of $\phi$, which in this case would be a aver…
328 \langle \phi \rangle(x,y) = \frac{1}{L_z + (T_f - T_0)}\int_0^{L_z} \int_{T_0}^{T_f} \phi(x, y, z, …
337 The function $\langle \phi \rangle (x,y)$ is represented on a 2-D finite element grid, taken from t…
349 \langle \phi \rangle_z(x,y,t) = \frac{1}{L_z} \int_0^{L_z} \phi(x, y, z, t) \mathrm{d}z
352 where the function $\phi$ may be the product of multiple solution functions and $\langle \phi \rang…
359 Substituting the spanwise average of $\phi$ for $u$, we get:
362 \bm M [\langle \phi \rangle_z]_N = \int_0^{L_x} \int_0^{L_y} \left [\frac{1}{L_z} \int_0^{L_z} \phi…
368 \bm M [\langle \phi \rangle_z]_N = \frac{1}{L_z} \int_\Omega \phi(x,y,z,t) \psi^\mathrm{parent}_N(x…
378 At the beginning of each simulation, the time integral of a statistic is set to 0, $\overline{\phi}…
381 $$\overline{\phi}_\mathrm{new} = \overline{\phi}_{\mathrm{old}} + \phi(t_\mathrm{new}) \Delta T$$
382 where $\phi(t_\mathrm{new})$ is the statistic at the current time and $\Delta T$ is the time since …
388 \bm M [\langle \phi \rangle]_N = \frac{1}{L_z + (T_f - T_0)} \int_\Omega \int_{T_0}^{T_f} \phi(x,y,…
390 where the integral $\int_{T_0}^{T_f} \phi(x,y,z,t) \mathrm{d}t$ is calculated on a running basis.
423 \langle \phi' \theta' \rangle = \langle \phi \theta \rangle - \langle \phi \rangle \langle \theta \…
434 \overline{\phi} - \nabla \cdot (\beta (\bm{D}\bm{\Delta})^2 \nabla \overline{\phi} ) = \phi
437 for $\phi$ the scalar solution field we want to filter, $\overline \phi$ the filtered scalar soluti…
441 \int_\Omega \left( v \overline \phi + \beta \nabla v \cdot (\bm{D}\bm{\Delta})^2 \nabla \overline \…
442 - \cancel{\int_{\partial \Omega} \beta v \nabla \overline \phi \cdot (\bm{D}\bm{\Delta})^2 \bm{\hat…
443 \int_\Omega v \phi \, , \; \forall v \in \mathcal{V}_p
446 …assume that $(\bm{D}\bm{\Delta})^2 = \bm{0} \Leftrightarrow \overline \phi = \phi$ at boundaries (…
486 The filtering at the wall may also be damped, to smoothly meet the $\overline \phi = \phi$ boundary…
726 …qrt{q^n(\bm{x})} \bm{\sigma}^n \cos(\kappa^n \bm{d}^n \cdot \bm{\hat{x}}^n(\bm{x}, t) + \phi^n ) \\
732 \bm{d}^n, \phi^n\}_{n=1}^N$, the Cholesky decomposition of the Reynolds stress
843 \bm{d}^n, \phi^n\}_{n=1}^N$. It has the format:
846 [d_1] [d_2] [d_3] [phi] [sigma_1] [sigma_2] [sigma_3]
854 | $ \{\bm{\sigma}^n, \bm{d}^n, \phi^n\}_{n=1}^N$ | RN Set   | No             | Yes       |