Changes between Version 46 and Version 47 of doc/tec/bc

Timestamp:

Nov 19, 2018 9:17:47 AM (6 years ago)

Author:

suehring

Comment:

--

doc/tec/bc

@@ -261 +261 @@
 
 
-== Open outflow boundary conditions ==
-At the outflow boundary (outlet), the velocity components ''u,,i,,'' meet radiation boundary conditions, viz.
-{{{
-#!Latex
-\begin{align*}
-\frac{\partial u_i}{\partial t} + U_{u_i} \frac{\partial u_i}{\partial n} = 0\,,
-\end{align*}
-}}}
-as proposed by [#orlanski1976 Orlanski (1976)]. Here ''∂/∂n'' is the derivative normal to the outlet (i.e., ''∂/∂x'' in Figure 2 and ''U,,ui,,'' a transport velocity which includes wave propagation and advection. Rewriting the equation above yields the transport velocity
-{{{
-#!Latex
-\begin{align*}
-U_{u_i} = -\left(\frac{\partial u_i}{\partial t}\right)\left(\frac{\partial u_i}{\partial n}\right)^{-1}
-\end{align*}
-}}}
-that is calculated at interior grid points next to the outlet at the preceding time step for each velocity component. If the transport velocity, calculated by means of the equation for the transport velocity, is outside the range ''0 ≤ U,,ui,, ≤ '''Δ'''/Δt'', it is set to the respective threshold value that is exceeded. Because this local determination of ''U,,ui,,'' can show high variations in case of complex turbulent flows, it is averaged laterally to the direction of the outflow, so that it varies only in the vertical direction. Alternatively, the transport velocity can be set to the upper threshold value (''U,,ui,, = '''Δ'''/Δt'') for the entire outlet. Both equations mentioned in this section are discretized using an upstream method following [#miller1981 Miller and Thorpe (1981)]. As the radiation boundary condition does not ensure conservation of mass, a mass flux correction can be applied at the outlet (see [wiki:/doc/tec/noncyclic#Massfluxcorrection mass flux correction]). For more information about the outflow boundary see Sect. [wiki:/doc/tec/noncyclic#Outflowboundary outflow boundary].
-
-
 == Synthetic Turbulence Generator ==
 Since r2259 a synthetic turbulence generator is implemented in PALM to generate a turbulent inflow condition. The method is based on the work of [#xie2008 Xie and Castro (2008)] and [#kim2013 Kim et al. (2013)]. Unscaled turbulent motions ''u,,*i,,'' are calculated via a statistical method based on length scales along each direction and scaled with an amplitude tensor ''a,,ij,,'' based on a prescribed Reynolds stress tensor. The calculated turbulence is then added to a fixed mean profile ''U,,i,,'' at the inflow boundary:
@@ -326 +308 @@
 '''Method 2:''' In many cases, however, detailed information about the Reynolds stress and turbulent length scales are not available, so that these information need to be parametrized. If no ASCII input file is provided, this will be done automatically. Further, turbulence statistics will be adjusted automatically, so that the turbulence generator can account for non-stationary situations. Parametrization of the Reynolds stress follows [#rotach1996 Rotach et al. (1996)].
 An description of the applied turbulence parametrization will follow soon. 
+
+== Open outflow boundary conditions ==
+At the outflow boundary (outlet), the velocity components ''u,,i,,'' meet radiation boundary conditions, viz.
+{{{
+#!Latex
+\begin{align*}
+\frac{\partial u_i}{\partial t} + U_{u_i} \frac{\partial u_i}{\partial n} = 0\,,
+\end{align*}
+}}}
+as proposed by [#orlanski1976 Orlanski (1976)]. Here ''∂/∂n'' is the derivative normal to the outlet (i.e., ''∂/∂x'' in Figure 2 and ''U,,ui,,'' a transport velocity which includes wave propagation and advection. Rewriting the equation above yields the transport velocity
+{{{
+#!Latex
+\begin{align*}
+U_{u_i} = -\left(\frac{\partial u_i}{\partial t}\right)\left(\frac{\partial u_i}{\partial n}\right)^{-1}
+\end{align*}
+}}}
+that is calculated at interior grid points next to the outlet at the preceding time step for each velocity component. If the transport velocity, calculated by means of the equation for the transport velocity, is outside the range ''0 ≤ U,,ui,, ≤ '''Δ'''/Δt'', it is set to the respective threshold value that is exceeded. Because this local determination of ''U,,ui,,'' can show high variations in case of complex turbulent flows, it is averaged laterally to the direction of the outflow, so that it varies only in the vertical direction. Alternatively, the transport velocity can be set to the upper threshold value (''U,,ui,, = '''Δ'''/Δt'') for the entire outlet. Both equations mentioned in this section are discretized using an upstream method following [#miller1981 Miller and Thorpe (1981)]. As the radiation boundary condition does not ensure conservation of mass, a mass flux correction can be applied at the outlet (see [wiki:/doc/tec/noncyclic#Massfluxcorrection mass flux correction]). For more information about the outflow boundary see Sect. [wiki:/doc/tec/noncyclic#Outflowboundary outflow boundary].