Changes between Version 20 and Version 21 of doc/tec/bc

Timestamp:

May 4, 2016 8:54:50 AM (9 years ago)

Author:

Giersch

Comment:

--

doc/tec/bc

@@ -229 +229 @@
 
 == Turbulence recycling ==
-If non-cyclic horizontal boundary conditions are used, PALM offers the possibility of generating time-dependent turbulent inflow data by using a turbulence recycling method. The method follows the one described by [#lund1998 Lund et al. (1998)], with the modifications introduced by [#kataoka2002 Kataoka and Mizuno (2002)]. Figure 3 gives an overview of the recycling method used in PALM.
+If non-cyclic horizontal boundary conditions are used, PALM offers the possibility of generating time-dependent turbulent inflow data by using a turbulence recycling method. The method follows the one described by [#lund1998 Lund et al. (1998)], with the modifications introduced by [#kataoka2002 Kataoka and Mizuno (2002)]. Figure 2 gives an overview of the recycling method used in PALM.
 
 [[Image(03.png,600px,border=1)]]
@@ -256 +256 @@
 sufficiently downstream of ''x'',,recycle,, to prevent effects on the turbulence at the inlet.
 
+
 == 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.
 
 == Topography ==
@@ -276 +292 @@
   cylinder using inflow turbulence. Wind Struct. 5: 379–392.
 
-
+* [=#orlanski1976] '''Orlanski I.''' 1976. A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21: 251–269.
+
+* [=#miller1981] ''' Miller MJ, Thorpe AJ.''' 1981. Radiation conditions for the lateral boundaries of limited-area numerical models. Q. J. Roy. Meteor. Soc. 107: 615–628.
+