Lines Matching refs:tau

186 …\tcolon\left(\frac{\partial \bm F_{\text{adv}}}{\partial \bm q}\right) \bm\tau \left( \frac{\parti…
203 …\tcolon\left(\frac{\partial \bm F_{\text{adv}}}{\partial \bm q}\right) \bm\tau \nabla \cdot \bm{F}…
210 In both {eq}`eq-weak-vector-ns-su` and {eq}`eq-weak-vector-ns-supg`, $\bm\tau \in \mathbb R^{5\time…
211 …plained via an ansatz for subgrid state fluctuations $\tilde{\bm q} = -\bm\tau \bm r$ where $\bm r…
227 :::{dropdown} Stabilization scale $\bm\tau$
246 \tau = \frac{\xi(\mathrm{Pe})}{\lVert \bm u_{\bm X} \rVert},
247 $$ (eq-tau-advdiff)
250 Note that $\tau$ has units of time and, in the transport-dominated limit, is proportional to elemen…
254 \nabla v \cdot \bm u \tau \bm u \cdot \nabla q = \nabla_{\bm X} v \cdot (\bm u_{\bm X} \tau \bm u_{…
260 #### Navier-Stokes $\tau$ definition
287 #### Advection-Diffusion $\tau$ definition
292 …\tau = \textrm{minreg}_2 \left\{\frac{\Delta t}{2 C_t},\ \frac{h}{aC_a}, \ \frac{h^2}{\kappa C_d} …
301 …\tau &= \textrm{minreg}_2 \left \{ \frac{\Delta t}{2 C_t}, \frac{1}{C_a \sqrt{\bm u \cdot (\bm u \…
309 #### Euler $\tau$ definition
313 \tau_{ii} = c_{\tau} \frac{2 \xi(\mathrm{Pe})}{(\lambda_{\max \text{abs}})_i \lVert \nabla_{x_i} \b…
314 $$ (eq-tau-conservative)
316 where $c_{\tau}$ is a multiplicative constant reported to be optimal at 0.5 for linear elements, $\…
390 This filtering operation results in an extra stress-like term, $\bm{\tau}^r$, representing the effe…
404      \bm{\tau}^r \\
405      \bm{u}  \cdot \bm{\tau}^r