Lines Matching refs:right

22 … \cdot \left( \frac{\bm{U} \otimes \bm{U}}{\rho} + P \bm{I}_3 -\bm\sigma \right) - \rho \bm{b}  &=…
23 …\left( \frac{(E + P)\bm{U}}{\rho} -\bm{u} \cdot \bm{\sigma} - k \nabla T \right) - \rho \bm{b} \cd…
31 P = \left( {c_p}/{c_v} -1\right) \left( E - {\bm{U}\cdot\bm{U}}/{(2 \rho)} \right) \, ,
86 …\bm{q}_N}{\partial t} + \nabla \cdot \bm{F}(\bm{q}_N) - \bm{S}(\bm{q}_N) \right) \,dV = 0 \, , \; …
95 \int_{\Omega} \bm v \cdot \left( \frac{\partial \bm{q}_N}{\partial t} - \bm{S}(\bm{q}_N) \right)  \…
127      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)\\
179 …\int_{\Omega} \bm v \cdot \left( \frac{\partial \bm{q}_N}{\partial t} - \bm{S}(\bm{q}_N) \right)  …
182 …+ \int_{\Omega} \nabla\bm v \tcolon\left(\frac{\partial \bm F_{\text{adv}}}{\partial \bm q}\right)…
183   \nabla \cdot \bm{F} \, (\bm{q}_N) - \bm{S}(\bm{q}_N) \right) \,dV &= 0
196 …\int_{\Omega} \bm v \cdot \left( \frac{\partial \bm{q}_N}{\partial t} - \bm{S}(\bm{q}_N) \right)  …
199 …+ \int_{\Omega} \nabla\bm v \tcolon\left(\frac{\partial \bm F_{\text{adv}}}{\partial \bm q}\right)…
273 \mathcal{F} = \sqrt{ \rho^2 \left [ \left(\frac{2C_t}{\Delta t}\right)^2
274 + \bm u \cdot (\bm u \cdot  \bm g)\right]
284 \tau = \left [ \left(\frac{2 C_t}{\Delta t}\right)^2
286 + \frac{\kappa^2 \Vert \bm g \Vert_F ^2}{C_d} \right]^{-1/2}
362 …\int_0^{L_y} \left [\frac{1}{L_z} \int_0^{L_z} \phi(x,y,z,t) \mathrm{d}z \right ] \psi^\mathrm{par…
365 The triple integral in the right hand side is just an integral over the full domain
403 …e mathematical definition on the left and the label (present in CGNS output files) is on the right.
441 …\overline \phi + \beta \nabla v \cdot (\bm{D}\bm{\Delta})^2 \nabla \overline \phi \right) \,d\Omega
490 \zeta = 1 - \exp\left(-\frac{y^+}{A^+}\right)
562 …}{\partial t} + \nabla \cdot \left( \frac{\bm{U} \otimes \bm{U}}{\rho} + P \bm{I}_3 \right) &= 0 \\
563 \frac{\partial E}{\partial t} + \nabla \cdot \left( \frac{(E + P)\bm{U}}{\rho} \right) &= 0 \, , \\
597 …c{h_{SHOCK}}{2u_{cha}} \left( \frac{ \,|\, \nabla \rho \,|\, h_{SHOCK}}{\rho_{ref}} \right)^{\beta}
603 h_{SHOCK} = 2 \left( C_{YZB} \,|\, \bm p \,|\, \right)^{-1}
623 \rho &= \rho_\infty\left(1+A\exp\left(\frac{-(\bar{x}^2 + \bar{y}^2)}{2\sigma^2}\right)\right) \\
625 …amma -1}\left(1+A\exp\left(\frac{-(\bar{x}^2 + \bar{y}^2)}{2\sigma^2}\right)\right) + \frac{\bm U_…
641 … boundary conditions at the inflow (left) and Riemann-type outflow on the right, with exterior ref…
678 $$ u_1 = u_{\max} \left [ 1 - \left ( \frac{x_2}{H}\right)^2 \right] \quad \quad u_2 = u_3 = 0$$
679 …T_w \left [ 1 + \frac{Pr \hat{E}c}{3} \left \{1 - \left(\frac{x_2}{H}\right)^4  \right \} \right]$$
727 \bm{\hat{x}}^n &= \left[(x - U_0 t)\max(2\kappa_{\min}/\kappa^n, 0.1) , y, z  \right]^T
760 f_\eta = \exp \left[-(12\kappa /\kappa_\eta)^2 \right], \quad
761 …ft( - \left [ \frac{4\max(\kappa-0.9\kappa_\mathrm{cut}, 0)}{\kappa_\mathrm{cut}} \right]^3 \right)
873 S(\bm{q}) = -\sigma(\bm{x})\left.\frac{\partial \bm{q}}{\partial \bm{Y}}\right\rvert_{\bm{q}} \bm{Y…
915 …rho_0 V_0^2}{16} \left ( \cos(2 \hat x) + \cos(2 \hat y)\right) \left( \cos(2 \hat z) + 2 \right) …