\form#0:$ \vect{\varia} $
\form#1:$ \vect{Rhs} $
\form#2:\[ \vect{Rhs} = \vect{Rhs} - \sum_{\fij \in \Facei{\celli}} \left( \dot{m}_\ij \left( \vect{\varia}_\fij - \vect{\varia}_\celli \right) - \mu_\fij \gradt_\fij \vect{\varia} \cdot \vect{S}_\ij \right) \]
\form#3:$ \mu \transpose{\gradt\vect{\varia}} + \lambda \trace{\gradt\vect{\varia}} $
\form#4:$ \lambda $
\form#5:$ -\frac{2}{3} \mu $
\form#6:$ \divv \left(\mu \gradt \transpose{\vect{a}} \right) -2/3 \grad\left( \mu \dive \vect{a} \right)$
\form#7:$ \mu_\fij \dfrac{S_\fij}{\ipf \jpf} $
\form#8:$ \mu_\fib \dfrac{S_\fib}{\ipf \centf} $
\form#9:$ \varia $
\form#10:$ Rhs $
\form#11:\[ Rhs = Rhs - \sum_{\fij \in \Facei{\celli}} \left( \dot{m}_\ij \left( \varia_\fij - \varia_\celli \right) - \mu_\fij \gradv_\fij \varia \cdot \vect{S}_\ij \right) \]
\form#12:$ C_p $
\form#13:$ \tens{\mu}_\celli $
\form#14:\[ Rhs = Rhs + \sum_{\fij \in \Facei{\celli}} \left( C_p\dot{m}_\ij \varia_\fij - \lambda_\fij \gradv_\fij \varia \cdot \vect{S}_\ij \right) \]
\form#15:$ \der{u_i}{x_j} $
\form#16:\[ Rhs = Rhs - \sum_{\fij \in \Facei{\celli}} \left( - \tens{\mu}_\fij \gradv_\fij \varia \cdot \vect{S}_\ij \right) \]
\form#17:\[ \vect{Rhs} = \vect{Rhs} - \sum_{\fij \in \Facei{\celli}} \left( - \tens{\mu}_\fij \gradt_\fij \vect{\varia} \cdot \vect{S}_\ij \right) \]
\form#18:$ \tens{\mu}_\fij \dfrac{S_\fij}{\ipf \jpf} $
\form#19:$ \dfrac{S_\fib}{\ipf \centf} $
\form#20:$ \rho \vect{u} \cdot \vect{S}_\ij$
\form#21:$ \dot{m}_\ij $
\form#22:$ \grad \left(\rho \vect{u} \right) $
\form#23:$ \vect{A}_{\rho u} = \rho_\fib \vect{A}_u $
\form#24:$ \tens{B}_{\rho u} = \tens{B}_u $
\form#25:$ \tens{B}_{u} $
\form#26:\[ \dot{m}_\ib = \left[ \rho_\fib \vect{A}_u + \rho_\fib \tens{B}_u \vect{u} + \tens{B}_u \left(\gradv \vect{u} \cdot \vect{\centi \centip}\right)\right] \cdot \vect{S}_\ij \]
\form#27:$ \rho\vect{u}\cdot\vect{S} $
\form#28:$ \vect{u}\cdot\vect{S} $
\form#29:$ \dot{m}_\fij $
\form#30:$ \dot{m}_\fib $
\form#31:$ \rho \vect{u} \cdot \vect{s}_\ij$
\form#32:$ \gradt \left(\rho \vect{u} \right) $
\form#33:$ \vect{a}_{\rho u} = \rho_\fib \vect{a}_u $
\form#34:$ \tens{b}_{\rho u} = \tens{b}_u $
\form#35:\[ \dot{m}_\ib = \left[ \rho_\fib \vect{a}_u + \rho_\fib \tens{b}_u \vect{u} + \tens{b}_u \left(\gradt \vect{u} \cdot \vect{\centi \centip}\right)\right] \cdot \vect{s}_\ij \]
\form#36:$ \rho\vect{u}\cdot\vect{s} $
\form#37:$ \vect{u}\cdot\vect{s} $
\form#38:$ \sum_{\fij \in \Facei{\celli}} \dot{m}_\fij $
\form#39:\[ \sum_{\fij \in \Facei{\celli}} \dot{m}_\fij = \sum_{\fij \in \Facei{\celli}} \dot{m}_\fij - \sum_{\fij \in \Facei{\celli}} \left( \tens{\mu}_\fij \gradv_\fij P \cdot \vect{S}_\ij \right) \]
\form#40:$ P $
\form#41:\[ \dot{m}_\fij = \dot{m}_\fij - \left( \tens{\mu}_\fij \gradv_\fij P \cdot \vect{S}_\ij \right) \]
\form#42:$ S_\fib $
\form#43:$ v_a \cdot v_b $
\form#44:\[ v_a \cdot v_b = \sum_{\celli =1}^{\ncell} v_{a_\celli} v_{b_\celli} \]
\form#45:\[ v_a \cdot v_b = \sqrt{\sum_{\celli =1}^{\ncell} v_{a_\celli} v_{b_\celli}} \]
\form#46:\[ v_a \cdot v_b = \sum_{\celli =1}^{\ncell} \dfrac{v_{a_\celli} v_{b_\celli}}{\norm{\vol{\celli}}} \]
\form#47:\[ v_a \cdot v_b = \sqrt{\sum_{\celli =1}^{\ncell} \dfrac{v_{a_\celli} v_{b_\celli}}{\norm{\vol{\celli}}}} \]
\form#48:$ \frac{\vect{IF} \cdot \tens{K}_\celli} {\norm{\tens{K}_\celli \cdot \vect{S}}^2} $
\form#49:$ \frac{\vect{FJ} \cdot \tens{K}_\cellj} {\norm{\tens{K}_\cellj \cdot \vect{S}}^2} $
\form#50:$ \vect{u} \cdot \vect{n} = 0 $
\form#51:$ (\mu+\mu_T) \gradv \vect{u} \cdot \vect{n} $
\form#52:$ \Delta t \grad P \cdot \vect{n} $
\form#53:$ cp \left( K + \dfrac{K_T}{\sigma_T} \right) \grad T \cdot \vect{n} $
\form#54:$ \divs ( \grad P ) = \divs ( f ) $
\form#55:$ \varia^\theta = \theta \varia^{n+1} + (1-\theta)\varia^n $
\form#56:$ \fib $
\form#57:$ \centf $
\form#58:$ Q $
\form#59:\[ P_\centf = A_P^g + B_P^g P_\centi \]
\form#60:\[ Q_\centf = A_P^f + B_P^f P_\centi \]
\form#61:$ P_\centi $
\form#62:$ \vect{u} $
\form#63:\[ \vect{u}_\centf = \vect{A}_u^g + \tens{B}_u^g \vect{u}_\centi \]
\form#64:\[ \vect{Q}_\centf = \vect{A}_u^f + \tens{B}_u^f \vect{u}_\centi \]
\form#65:$ \tens{B}_u^g $
\form#66:$ \tens{B}_u^f $
\form#67:$ \centip $
\form#68:$ R_{ij} $
\form#69:$ a $
\form#70:\[ f_s^{imp}(a^{n+1}-a^n) + \divs \left( a^{n+1} \rho \vect{u} - \mu \grad a^{n+1} \right) = Rhs \]
\form#71:\[ f_s^{imp} \delta a + \divs \left( \delta a \rho \vect{u} - \mu \grad \delta a \right) = Rhs^1 \]
\form#72:$ \delta a = a^{n+1} - a^n$
\form#73:$ Rhs^1 = Rhs - \divs( a^n \rho \vect{u} - \mu \grad a^n)$
\form#74:\[ f_s^{imp} \delta a^k + \divs \left(\delta a^k \rho \vect{u}-\mu\grad\delta a^k \right) = Rhs^k \]
\form#75:$Rhs^k=Rhs-f_s^{imp}(a^k-a^n) - \divs \left( a^k\rho\vect{u}-\mu\grad a^k \right)$
\form#76:$ f_s^{imp} $
\form#77:$ \delta \varia^k $
\form#78:$ \delta \varia^{k-1} $
\form#79:$ a^n $
\form#80:$ a^k $
\form#81:$ Rhs^k $
\form#82:$ \vect{a} $
\form#83:\[ \tens{f_s}^{imp}(\vect{a}^{n+1}-\vect{a}^n) + \divv \left( \vect{a}^{n+1} \otimes \rho \vect {u} - \mu \gradt \vect{a}^{n+1}\right) = \vect{Rhs} \]
\form#84:\[ \tens{f_s}^{imp} \delta \vect{a} + \divv \left( \delta \vect{a} \otimes \rho \vect{u} - \mu \gradt \delta \vect{a} \right) = \vect{Rhs}^1 \]
\form#85:$ \delta \vect{a} = \vect{a}^{n+1} - \vect{a}^n$
\form#86:$ \vect{Rhs}^1 = \vect{Rhs} - \divv \left( \vect{a}^n \otimes \rho \vect{u} - \mu \gradt \vect{a}^n \right)$
\form#87:\[ \tens{f_s}^{imp} \delta \vect{a}^k + \divv \left( \delta \vect{a}^k \otimes \rho \vect{u} - \mu \gradt \delta \vect{a}^k \right) = \vect{Rhs}^k \]
\form#88:$ \vect{Rhs}^k = \vect{Rhs} - \tens{f_s}^{imp} \left(\vect{a}^k-\vect{a}^n \right) - \divv \left( \vect{a}^k \otimes \rho \vect{u} - \mu \gradt \vect{a}^k \right)$
\form#89:$ \tens{f_s}^{imp} $
\form#90:$ \delta \vect{\varia}^k $
\form#91:$ \delta \vect{\varia}^{k-1} $
\form#92:$ \vect{a}^n $
\form#93:$ \vect{a}^k $
\form#94:$ \vect{Rhs}^k $
\form#95:\[ \delta P_\centf = B_P^g \delta P_\centi \]
\form#96:\[ \delta Q_\centf = B_P^f \delta P_\centi \]
\form#97:$ \Gamma^n $
\form#98:$ 10^{-12}$
\form#99:$ 10^{+30}$
\form#100:$ 10^{+12}$
\form#101:$ 0 $
\form#102:$ \pi $
\form#103:$\sigma$
\form#104:$W.m^{-2}.K^{-4}$
\form#105:$P0$
\form#106:$T0$
\form#107:$P$
\form#108:$P^*=P-\rho_0\vect{g}.(\vect{x}-\vect{x}_0)+P^*_0-P_0$
\form#109:$\vect{x_0}$
\form#110:$P^*_0$
\form#111:$P_0$
\form#112:$-\grad{P}+\rho\vect{g}$
\form#113:$-\grad{P^*}+(\rho-\rho_0)\vect{g}$
\form#114:$\rho$
\form#115:$P^*$
\form#116:$\vect{x}_0$
\form#117:$ kg/mol $
\form#118:$k-\varepsilon$
\form#119:$R_{ij}-\varepsilon$
\form#120:$k-\omega$
\form#121:$ \dfrac{1}{\kappa} \ln(y^+) + cstlog $
\form#122:$ cstlog = 5.2 $
\form#123:$y^+$
\form#124:$1/\kappa\approx 2,38$
\form#125:$C_\mu$
\form#126:$ C_\mu^\frac{1}{4} $
\form#127:$C_{\varepsilon 1}$
\form#128:$C_{\varepsilon 2}$
\form#129:$C_{\varepsilon 4}$
\form#130:$k$
\form#131:$\varepsilon$
\form#132:$C_1$
\form#133:$C_2$
\form#134:$C_3$
\form#135:$C_1^\prime$
\form#136:$C_2^\prime$
\form#137:$C_{s1}$
\form#138:$C_{s2}$
\form#139:$C_{r1}$
\form#140:$C_{r2}$
\form#141:$C_{r3}$
\form#142:$C_{r4}$
\form#143:$C_s$
\form#144:$\sigma_{k1}$
\form#145:$\sigma_{k2}$
\form#146:$\sigma_{\omega 1}$
\form#147:$\sigma_{\omega 2}$
\form#148:$\beta_1$
\form#149:$\beta_2$
\form#150:$\frac{\beta_1}{C_\mu}-\frac{\kappa^2}{\sqrt{C_\mu}\sigma_{\omega 1}}$
\form#151:$\gamma_1$
\form#152:$\kappa$
\form#153:$\frac{\beta_2}{C_\mu}-\frac{\kappa^2}{\sqrt{C_\mu}\sigma_{\omega 2}}$
\form#154:$\gamma_2$
\form#155:$a_1$
\form#156:$ c_1 $
\form#157:$ \delta = \text{xlesfl} . (\text{ales} . volume)^{\text{bles}} $
\form#158:$\Omega_i$
\form#159:$\overline{\Delta}=xlesfl(ales*|\Omega_i|)^{bles}$
\form#160:$\displaystyle\mu_{sg}= \rho C_{smago}^2\bar{\Delta}^2\sqrt{2\bar{S}_{ij}\bar{S}_{ij}}$
\form#161:$\bar{\Delta}$
\form#162:$\bar{S}_{ij}$
\form#163:$\widetilde{\overline{\Delta}}=xlesfd\overline{\Delta}$
\form#164:$C$
\form#165:$ smagmx^2$
\form#166:$ (1-\exp^{(-y^+/cdries}) $
\form#167:$\varphi$
\form#168:$C_T$
\form#169:$C_L$
\form#170:$C_\eta$
\form#171:$ k $
\form#172:$ \varepsilon $
\form#173:$ \omega $
\form#174:$ \varphi $
\form#175:$ \overline{f} $
\form#176:$ \alpha $
\form#177:$ \nu_T $
\form#178:\[ \divs ( \grad \varia ) = -1 \]
\form#179:$ \varia_|b = 0 $
\form#180:$ \grad \varia \cdot \vect{n} = 0 $
\form#181:\[ d \simeq -|\grad \varia | + \sqrt{ \grad \varia \cdot \grad \varia +2 \varia } \]
\form#182:\[ \dfrac{\partial \varia}{\partial t} + \divs \left( \varia \vect{V} \right) - \divs \left( \vect{V} \right) \varia = 0 \]
\form#183:$ \vect{V} $
\form#184:\[ \vect{V} = \dfrac{ \grad y }{\norm{\grad y} } \]
\form#185:\[ \varia = \dfrac{u_\star}{\nu} \textrm{ on walls} \]
\form#186:\[ \dfrac{\partial \varia}{\partial n} = 0 \textrm{ elsewhere} \]
\form#187:\[ y^+ = y \varia \]
\form#188:$ y^+ $
\form#189:$R_{ij}$
\form#190:$\omega$
\form#191:$\overline{f}$
\form#192:$\ne$
\form#193:$ \texttt{ush001}$
\form#194:$\texttt{ush002}$
\form#195:$\texttt{ush003}$
\form#196:$ \texttt{ush001.n\_0001} $
\form#197:$ \texttt{ush010.n\_0001} $
\form#198:$ \texttt{ush001.n\_0002} $
\form#199:$ \texttt{ush010.n\_0002} $
\form#200:$ \texttt{usrf01} $
\form#201:$ \texttt{usrf10} $
\form#202:$ \texttt{usrf01.n\_0001} $
\form#203:$ \texttt{usrf10.n\_0001} $
\form#204:$ \texttt{usrf01.n\_0002} $
\form#205:$ \texttt{usrf10.n\_0002} $
\form#206:$ W\,m^{-2} $
\form#207:$ y^+ = \dfrac{\centip \centf u_\star}{\nu}$
\form#208:\[ h_{tur} = Pr \dfrac{y^+}{T^+} \]
\form#209:$ T^+ $
\form#210:\[ h = \dfrac{K}{\centip \centf} h_{tur} \]
\form#211:$ \vect{IJ}$
\form#212:$\vect{n}$
\form#213:$\vect{IF}$
\form#214:$\displaystyle\frac{\vect{FJ}.\vect{n}}{\vect{IJ}.\vect{n}}$
\form#215:$\vect{I'J'}$
\form#216:$\vect{II'}$
\form#217:$\vect{OF}$
\form#218:$ u_x $
\form#219:$ u_y $
\form#220:$ u_z $
\form#221:$ R_{xx} $
\form#222:$ R_{yy} $
\form#223:$ R_{zz} $
\form#224:$ R_{xy} $
\form#225:$ R_{yz} $
\form#226:$ \phi $
\form#227:$ \phi-f_b $
\form#228:$ f_b $
\form#229:$ Bl-v^2-k $
\form#230:$ k-\omega $
\form#231:$ \widetilde{\nu}_T $
\form#232:$ w_x $
\form#233:$ w_y $
\form#234:$ w_z $
\form#235:$ P_{tot} = P^\star +\rho \vect{g} \cdot (\vect{x}-\vect{x}_0) $
\form#236:$ \tens{R}_{ij} $
\form#237:$ \rho $
\form#238:$ \mu $
\form#239:$ \theta $
\form#240:$ \theta_S $
\form#241:$ \vect{u}^{k+1} - \vect{u}^k $
\form#242:$ \vect{u}^0 $
\form#243:$ k-\varepsilon $
\form#244:$ R_{ij}-\epsilon $
\form#245:$ BL-v^2-k $
\form#246:$ 2/3 \rho \grad k $
\form#247:$ k- \varepsilon $
\form#248:$ R_{ij}- \varepsilon $
\form#249:$ \divv \left( \rho \tens{R} \right) $
\form#250:$ \tens{R} $
\form#251:$ \overline{\varia^\prime \vect{u}^\prime} $
\form#252:$ \divs \left( \mu \transpose{\gradt \, \vect{u}} - 2/3 \mu \trace{\gradt \, \vect{u}} \right) $
\form#253:$ (k, \varepsilon, R_{ij}, \omega, \varphi, \overline{f}, \alpha, \nu_t$
\form#254:$\displaystyle \frac{\partial }{\partial n}\left(\frac{ \partial P}{\partial \tau}\right)=0$
\form#255:$\vect{u}^*$
\form#256:$\eta^{\,pred}_{\,i,k}(\vect{u}^*)$
\form#257:$ \Omega_i $
\form#258:$\vect{\mathcal R}^{\,pred}(\vect{u}^*)$
\form#259:$\vect{u}$
\form#260:\begin{eqnarray*} \vect{\mathcal R}^{\,pred}(\vect{u}^*) & = & \rho^n \dfrac{\vect{u}^*-\vect{u}^n}{\Delta t} + \rho^n \vect{u}^n \cdot \gradt (\vect{u}^*) - \divv \left((\mu+\mu_t)^n \gradt (\vect{u}^*) \right) + \grad(P^n) \\ & - & \text{rest of the right-hand member } (\vect{u}^n, P^n, \text{other variables}^n) \end{eqnarray*}
\form#261:$ \eta^{\,pred}_{\,i,k}(\vect{u}^*)= {|\Omega_i|}^{\,(k-2)/2}\ ||\vect{\mathcal R}^{\,pred}(\vect{u}^*)|| _{{IL}^{2}(\Omega_i)} $
\form#262:$ |\Omega_i| $
\form#263:$ {IL}^{2}(\Omega_i) $
\form#264:$ \eta^{\,pred}_{\,i,k}(\vect{u}^*)$
\form#265:$\eta^{\,der}_{\,i,k}(\vect{u}^{\,n+1})$
\form#266:\begin{eqnarray*} \eta^{\,der}_{\,i,k}(\vect{u}^{\,n+1}) &=& {|\Omega_i|}^{(k-2)/2} || \divs (\text{corrected mass flow after the pressure step}) - \Gamma||_{{L}^{2}(\Omega_i)} \\ &=& {|\Omega_i|}^{(1-k)/2} | \divs (\text{corrected mass flow after the pressure step})- \Gamma| \end{eqnarray*}
\form#267:$ \eta^{\,corr}_{\,i,k}(\vect{u}^{\,n+1})$
\form#268:\begin{eqnarray*} \eta^{\,corr}_{\,i,k}(\vect{u}^{\,n+1})= |\Omega_i|^{\,\delta_{\,2,k}}\ |div (\rho^n \vect{u}^{n+1}) - \Gamma| \end{eqnarray*}
\form#269:$\vect{u}^{n+1}$
\form#270:$ \,\delta_{\,2,k}$
\form#271:$kg.s^{\,-1}$
\form#272:$ \eta^{\,tot}_{\,i,k}(\vect{u}^{\,n+1})$
\form#273:$\vect{\mathcal R}^{\,tot}(\vect{u}^{\,n+1})$
\form#274:$ \eta^{\,tot}_{\,i,k}(\vect{u}^{\,n+1})= {|\Omega_i|}^{\,(k-2)/2}\ ||\vect{\mathcal R}^{\,tot}(\vect{u}^{\,n+1})|| _{{I\hspace{-.25em}L}^{2}(\Omega_i)} $
\form#275:$ \vect{u} \cdot \vect{S} = \vect{w} \cdot \vect{S} $
\form#276:$S^2=2S_{ij}^D S_{ij}^D$
\form#277:$div(\vect{u})$
\form#278:$S^2$
\form#279:$W.m^{-2}.K^.$
\form#280:$W.m^{-2}$
\form#281:$\rho C_p$
\form#282:$J.m^{-3}.K^{-1}$
\form#283:\[ D \left( \Delta t, \varia \right) = \divs \left( \rho \vect{u}^n\right) - \Gamma^n + \dfrac{\rho^n - \rho^{n-1}}{\Delta t} \]
\form#284:\[ \dot{m}^{n+\frac{1}{2}}_\ij = \dot{m}^{n}_\ij - \Delta t \grad_\fij \varia \cdot \vect{S}_\ij \]
\form#285:$ P_{hydro} $
\form#286:\[ \rho^n \dfrac{(\vect{u}^{hydro} - \vect{u}^n)}{\Delta t} = \rho^n \vect{g}^n - \grad P_{hydro} \]
\form#287:\[ \rho^n \divs \left( \delta \vect{u}_{hydro} \right) = 0 \]
\form#288:$ \delta \vect{u}_{hydro} = ( \vect{u}^{hydro} - \vect{u}^n) $
\form#289:\[ \divs \left( K \grad P_{hydro} \right) = \divs \left(\vect{g}\right) \]
\form#290:$ K $
\form#291:\[ K \equiv \dfrac{1}{\rho^n} \]
\form#292:\[ D_\fib \left( K, \, P_{hydro} \right) = \vect{g} \cdot \vect{n}_\ib \]
\form#293:$ \partial _x (P_{hydro}) $
\form#294:\[ D \left( \Delta t, \delta p \right) = \divs \left( \rho \vect{\widetilde{u}}\right) - \Gamma^n + \dfrac{\rho^n - \rho^{n-1}}{\Delta t} \]
\form#295:\[ \dot{m}^{n+1}_\ij = \dot{m}^{n}_\ij - \Delta t \grad_\fij \delta p \cdot \vect{S}_\ij \]
\form#296:$\kappa -2/3 \mu$
\form#297:\[ \grad( \kappa -2/3 \mu) \trace( \gradt(\vect{u})) ) \]
\form#298:$ \mu = \mu_{laminar} + \mu_{turbulent} $
\form#299:$ \kappa $
\form#300:\begin{eqnarray*} \der{\rho}{t} + \divs \left(\rho\vect{u}\right) &=&0 \\ \der{\rho \vect{u}}{t} + \divv \left(\vect{u}\otimes\rho\vect{u}\right)&=&0 \\ \der{E}{t} + \divs \left(\rho\vect{u} E\right) &=&0 \end{eqnarray*}
\form#301:$ f_{min} $
\form#302:$ f_{max} $
\form#303:$ J.kg^{-1}.K^{-1} $
\form#304:$K$
\form#305:$\text{\degresC}$
\form#306:$ kg.m^{-1}.s^{-1} $
\form#307:$T^3$
\form#308:$T^4$
\form#309:$CH_{X1m}$
\form#310:$CH_{X2m}$
\form#311:$O_2$
\form#312:$CO_2$
\form#313:$H_2O$
\form#314:$N_2$
\form#315:$ W/m^3 $
\form#316:$ C/m^3 $
\form#317:$ N/m^2 $
\form#318:$ A/m^2 $
\form#319:$ m^{-1} $
\form#320:\begin{eqnarray*} \tens{\sigma} = -P\,\tens{Id} + \mu (\grad\,\vect{u} + \ ^{t}\ggrad\,\vect{u}) +(\kappa-\frac{2}{3}\mu)\,\dive(\vect{u})\,\tens{Id} \end{eqnarray*}
\form#321:$\tens{\sigma}$
\form#322:\begin{eqnarray*} \left\{\begin{array}{lll} P_p=0 & \text{if} & 1 + \displaystyle\frac{\gamma-1}{2}M<0\\ P_p = P_i \left(1 + \displaystyle\frac{\gamma-1}{2}M\right) ^{\frac{2\gamma}{\gamma-1}} & \text{otherwise}\\ \end{array}\right.\\ \end{eqnarray*}
\form#323:\begin{eqnarray*} P_p = P_i \left(1 + \displaystyle\frac{\gamma(\gamma+1)}{4}M^2 +\gamma M \displaystyle\sqrt{1+\displaystyle\frac{(\gamma+1)^2}{16}M^2}\right) \end{eqnarray*}
\form#324:$M = \displaystyle\frac{\vect{u}_i \cdot \vect{n}}{c_i}$
\form#325:$\rho^{n+1}$\,=\,srrom\,$\rho^n$+(1-srrom)\,$\rho^{n+1}$
\form#326:$J/mol/K$
\form#327:$m^{-3}$
\form#328:$kg.m^{-1}.s^{-1}$
\form#329:$ R_{ij} - \varepsilon $
\form#330:$ R_{11} $
\form#331:$ R_{22} $
\form#332:$ R_{33} $
\form#333:$ R_{12} $
\form#334:$ R_{13} $
\form#335:$ R_{23} $
\form#336:$ k - \epsilon $
\form#337:$ k - \omega $
\form#338:$ R_{ij} - \epsilon $
\form#339:$ (\mu+\mu_T) \gradt \, \vect{u} \cdot \vect{n} $
\form#340:$ C_p = \left. \dfrac{\dd h}{\dd T}\right|_P $
\form#341:$ \mu_T $
\form#342:\[ \rho \norm{\vol{\celli}} \DP{\vect{u}} + .... = \tens{crvimp} \vect{u} + \vect{crvexp} \]
\form#343:$ \vect{u}_{fluid} \cdot \vect{n} = \vect{w}_{mesh} \cdot \vect{n} $
\form#344:$ \epsilon $
\form#345:\[ \begin{array}{r c l} Blance^n &=& \displaystyle \sum_{\celli=1}^{\ncell} \norm{\vol{\celli}} C_p \rho_\celli \left(T_\celli^{n-1} -T_\celli^n \right) \\ &+& \displaystyle \sum_{\fib} C_p \Delta t_\celli \norm{\vect{S}_\ib} \left(A_\ib^f + B_\ib^f T_\celli^n \right) \\ &+& \displaystyle \sum_{\fib} C_p \Delta t_\celli \dot{m}_\ib \left(A_\ib^g + B_\ib^g T_\celli^n \right) \end{array} \]
\form#346:\[ \rho^{n-1}_\celli = P_0 / \left( R T_\celli^{n-1} + T_0 \right) \]
\form#347:$ R$
\form#348:$ T_0 $
\form#349:$ \lambda/C_p $
