Lines Matching refs:t

13 \frac{\partial \rho}{\partial t} + \nabla \cdot \bm{U} &= 0 \\
14 \frac{\partial \bm{U}}{\partial t} + \nabla \cdot \left( \frac{\bm{U} \otimes \bm{U}}{\rho} + P \bm…
15 \frac{\partial E}{\partial t} + \nabla \cdot \left( \frac{(E + P)\bm{U}}{\rho} -\bm{u} \cdot \bm{\s…
31 \frac{\partial \bm{q}}{\partial t} + \nabla \cdot \bm{F}(\bm{q}) -S(\bm{q}) = 0 \, ,
79 \bm{q}_N (\bm{x},t)^{(e)} = \sum_{k=1}^{P}\psi_k (\bm{x})\bm{q}_k^{(e)}
88 \int_{\Omega} \bm v \cdot \left(\frac{\partial \bm{q}_N}{\partial t} + \nabla \cdot \bm{F}(\bm{q}_N…
97 \int_{\Omega} \bm v \cdot \left( \frac{\partial \bm{q}_N}{\partial t} - \bm{S}(\bm{q}_N) \right)  \…
111 <!-- TODO: This should be reframed in terms of PETSc TS's F(t, u, \dot u) = G(t, u) rather than spe…
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 \, ,
164 The scalar "shift" $\alpha$ scales inversely with the time step $\Delta t$, so small time steps res…
183 …\int_{\Omega} \bm v \cdot \left( \frac{\partial \bm{q}_N}{\partial t} - \bm{S}(\bm{q}_N) \right)  …
186 … F_{\text{adv}}}{\partial \bm q}\right) \bm\tau \left( \frac{\partial \bm{q}_N}{\partial t} \, + \,
200 …\int_{\Omega} \bm v \cdot \left( \frac{\partial \bm{q}_N}{\partial t} - \bm{S}(\bm{q}_N) \right)  …
279 \mathcal{F} = \sqrt{ \rho^2 \left [ \left(\frac{2C_t}{\Delta t}\right)^2
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 \…
302 …&= \left [ \left(\frac{2 C_t}{\Delta t}\right)^2 + C_a^2 \bm u \cdot (\bm u \cdot  \bm g) + \left(…
369 As noted, we can't calculate $\nabla \cdot \bm F_{\text{diff}}(\bm{q}_N)$ at quadrature points, so …
394 \frac{\partial \bm{\overline q}}{\partial t} + \nabla \cdot \bm{\overline F}(\bm{\overline q}) -S(\…
515 \bm{u}(\bm{x}, t) = \bm{\overline{u}}(\bm{x}) + \bm{C}(\bm{x}) \cdot \bm{v}'
520 …qrt{q^n(\bm{x})} \bm{\sigma}^n \cos(\kappa^n \bm{d}^n \cdot \bm{\hat{x}}^n(\bm{x}, t) + \phi^n ) \\
521 \bm{\hat{x}}^n &= \left[(x - U_0 t)\max(2\kappa_{\min}/\kappa^n, 0.1) , y, z  \right]^T