Lines Matching refs:F

31 \frac{\partial \bm{q}}{\partial t} + \nabla \cdot \bm{F}(\bm{q}) -S(\bm{q}) = 0 \, ,
54 \bm{F}(\bm{q}) &=
88 \int_{\Omega} \bm v \cdot \left(\frac{\partial \bm{q}_N}{\partial t} + \nabla \cdot \bm{F}(\bm{q}_N…
98 - \int_{\Omega} \nabla \bm v \!:\! \bm{F}(\bm{q}_N)\,dV & \\
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 …F$ represents contraction over both fields and spatial dimensions while a single dot represents co…
111 <!-- TODO: This should be reframed in terms of PETSc TS's F(t, u, \dot u) = G(t, u) rather than spe…
138 f(t^n, \bm{q}_N^n) = - [\nabla \cdot \bm{F}(\bm{q}_N)]^n + [S(\bm{q}_N)]^n \, .
184   - \int_{\Omega} \nabla \bm v \!:\! \bm{F}(\bm{q}_N)\,dV & \\
185   + \int_{\partial \Omega} \bm v \cdot \bm{F}(\bm{q}_N) \cdot \widehat{\bm{n}} \,dS & \\
187   \nabla \cdot \bm{F} \, (\bm{q}_N) - \bm{S}(\bm{q}_N) \right) \,dV &= 0
201   - \int_{\Omega} \nabla \bm v \!:\! \bm{F}(\bm{q}_N)\,dV & \\
202   + \int_{\partial \Omega} \bm v \cdot \bm{F}(\bm{q}_N) \cdot \widehat{\bm{n}} \,dS & \\
203 …{\partial \bm F_{\text{adv}}}{\partial \bm q}\right) \bm\tau \nabla \cdot \bm{F} \, (\bm{q}_N) \,dV
251 For advection-diffusion, $\bm F(q) = \bm u q$, and thus the SU stabilization term is
272 \tau_c &= \frac{C_c \mathcal{F}}{8\rho \trace(\bm g)} \\
273 \tau_m &= \frac{C_m}{\mathcal{F}} \\
274 \tau_E &= \frac{C_E}{\mathcal{F} c_v} \\
279 \mathcal{F} = \sqrt{ \rho^2 \left [ \left(\frac{2C_t}{\Delta t}\right)^2
372 \int_{\partial \Omega} \bm v \cdot \bm{F}_{\text{diff}}(\bm q_N) \cdot \widehat{\bm{n}} \,dS
373 - \int_{\Omega} \nabla \bm v \!:\! \bm{F}_{\text{diff}}(\bm{q}_N)\,dV
394 \frac{\partial \bm{\overline q}}{\partial t} + \nabla \cdot \bm{\overline F}(\bm{\overline q}) -S(\…
400 \bm{\overline F}(\bm{\overline q}) =
401 \bm{F} (\bm{\overline q}) +