Lines Matching refs:u

15 …dot \left( \frac{(E + P)\bm{U}}{\rho} -\bm{u} \cdot \bm{\sigma} - k \nabla T \right) - \rho \bm{b}…
19 where $\bm{\sigma} = \mu(\nabla \bm{u} + (\nabla \bm{u})^T + \lambda (\nabla \cdot \bm{u})\bm{I}_3)…
20 …mass density, $U$ the momentum density (defined as $\bm{U}=\rho \bm{u}$, where $\bm{u}$ is the vec…
40     \bm{U} \equiv \rho \bm{ u }\\
63  - \bm{u}  \cdot \bm{\sigma} - k \nabla T
69     \rho \bm{b}\cdot \bm{u}
111 <!-- TODO: This should be reframed in terms of PETSc TS's F(t, u, \dot u) = G(t, u) rather than spe…
228 A velocity vector $\bm u$ can be pulled back to the reference element as $\bm u_{\bm X} = \nabla_{\…
231 The ratio $\lVert \bm u \rVert / \lVert \bm u_{\bm X} \rVert$ is a covariant measure of (half) the …
236 The cell Péclet number is classically defined by $\mathrm{Pe}_h = \lVert \bm u \rVert h / (2 \kappa…
240 \mathrm{Pe} = \frac{\lVert \bm u \rVert^2}{\lVert \bm u_{\bm X} \rVert \kappa}.
251 For advection-diffusion, $\bm F(q) = \bm u q$, and thus the SU stabilization term is
254 \nabla v \cdot \bm u \tau \bm u \cdot \nabla q = \nabla_{\bm X} v \cdot (\bm u_{\bm X} \tau \bm u_{…
280 + \bm u \cdot (\bm u \cdot  \bm g)\right]
301 …rm{minreg}_2 \left \{ \frac{\Delta t}{2 C_t}, \frac{1}{C_a \sqrt{\bm u \cdot (\bm u \cdot  \bm g)}…
302 …&= \left [ \left(\frac{2 C_t}{\Delta t}\right)^2 + C_a^2 \bm u \cdot (\bm u \cdot  \bm g) + \left(…
324 where $u_i = \bm u \cdot \hat{\bm n}_i$ is the velocity component in direction $i$ and $a = \sqrt{\…
405      \bm{u}  \cdot \bm{\tau}^r
515 \bm{u}(\bm{x}, t) = \bm{\overline{u}}(\bm{x}) + \bm{C}(\bm{x}) \cdot \bm{v}'
611 …er by interpolation (for $l_t$, $\varepsilon$, $C_{ij}$, and $\overline{\bm u}$) or by calculation…
634 | $\bm{\overline{u}}$                            | ubar     | Yes            | No        |