Lines Matching refs:n
99 + \int_{\partial \Omega} \bm v \cdot \bm{F}(\bm q_N) \cdot \widehat{\bm{n}} \,dS
104 where $\bm{F}(\bm q_N) \cdot \widehat{\bm{n}}$ is typically replaced with a boundary condition.
107 …, $\bm v \cdot \bm S$ contracts over fields while $\bm F \cdot \widehat{\bm n}$ contracts over spa…
120 \bm{q}_N^{n+1} = \bm{q}_N^n + \Delta t \sum_{i=1}^{s} b_i k_i \, ,
127 k_1 &= f(t^n, \bm{q}_N^n)\\
128 k_2 &= f(t^n + c_2 \Delta t, \bm{q}_N^n + \Delta t (a_{21} k_1))\\
129 k_3 &= f(t^n + c_3 \Delta t, \bm{q}_N^n + \Delta t (a_{31} k_1 + a_{32} k_2))\\
131 k_i &= f\left(t^n + c_i \Delta t, \bm{q}_N^n + \Delta t \sum_{j=1}^s a_{ij} k_j \right)\\
138 f(t^n, \bm{q}_N^n) = - [\nabla \cdot \bm{F}(\bm{q}_N)]^n + [S(\bm{q}_N)]^n \, .
147 \bm f(\bm q_N) \equiv \bm g(t^{n+1}, \bm{q}_N, \bm{\dot{q}}_N) = 0 \, ,
185 + \int_{\partial \Omega} \bm v \cdot \bm{F}(\bm{q}_N) \cdot \widehat{\bm{n}} \,dS & \\
202 + \int_{\partial \Omega} \bm v \cdot \bm{F}(\bm{q}_N) \cdot \widehat{\bm{n}} \,dS & \\
232 … the direction of a unit vector $\hat{\bm n}$ is given by $\lVert \bigl(\nabla_{\bm X} \bm x\bigr)…
295 …oefficients, $h$ is the element length, and $\textrm{minreg}_n \{x_j\} = (\sum_j x_j^{-n})^{-1/n}$.
316 …al at 0.5 for linear elements, $\hat{\bm n}_i$ is a unit vector in direction $i$, and $\nabla_{x_i…
317 The flux Jacobian $\frac{\partial \bm F_{\text{adv}}}{\partial \bm q} \cdot \hat{\bm n}_i$ in each …
324 where $u_i = \bm u \cdot \hat{\bm n}_i$ is the velocity component in direction $i$ and $a = \sqrt{\…
329 …}} \Bigl( \frac{\partial \bm F_{\text{adv}}}{\partial \bm q} \cdot \hat{\bm n}_i \Bigr) = |u_i| + a
372 \int_{\partial \Omega} \bm v \cdot \bm{F}_{\text{diff}}(\bm q_N) \cdot \widehat{\bm{n}} \,dS
520 …' &= 2 \sqrt{3/2} \sum^N_{n=1} \sqrt{q^n(\bm{x})} \bm{\sigma}^n \cos(\kappa^n \bm{d}^n \cdot \bm{\…
521 \bm{\hat{x}}^n &= \left[(x - U_0 t)\max(2\kappa_{\min}/\kappa^n, 0.1) , y, z \right]^T
525 …n, \bm{d}^n, \phi^n\}_{n=1}^N$, the Cholesky decomposition of the Reynolds stress tensor $\bm{C}$ …
537 \kappa^n = \kappa_{\min} (1 + \alpha)^{n-1} \ , \quad \forall n=1, 2, ... , N
540 The wavemode amplitudes $q^n$ are defined by a model energy spectrum $E(\kappa)$:
543 q^n = \frac{E(\kappa^n) \Delta \kappa^n}{\sum^N_{n=1} E(\kappa^n)\Delta \kappa^n} \ ,\quad \Delta \…
595 kn[k^n];
611 …olation (for $l_t$, $\varepsilon$, $C_{ij}$, and $\overline{\bm u}$) or by calculation (for $q^n$).
622 …and.dat` file is the table of the random number set, $\{\bm{\sigma}^n, \bm{d}^n, \phi^n\}_{n=1}^N$.
631 | Math | Label | $f(\bm{x})$? | $f(n)$? |
633 | $ \{\bm{\sigma}^n, \bm{d}^n, \phi^n\}_{n=1}^N$ | RN Set | No | Yes |
640 | $q^n$ | q^n | Yes | Yes |
641 | $\{\kappa^n\}_{n=1}^N$ | k^n | No | Yes |