Changes between Version 66 and Version 67 of doc/tec/bc

Timestamp:

Jan 18, 2021 11:10:08 AM (4 years ago)

Author:

raasch

Comment:

--

doc/tec/bc

@@ -257 +257 @@
 \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].
+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. '''Since r4845, PALM is always using this upper threshold value.''' 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].
 
 
@@ -369 +369 @@
 === Outflow boundary ===
 
-At the outflow, an open boundary condition is needed to ensure that disturbances of the mean flow can exit the model domain without effecting the flow upstream. For the scalar quantities, Neumann boundary conditions are used at the outflow boundary which is the simplest way. For the velocity components, a Neumann condition would require to be considered in the solution of the Poisson equation for perturbation pressure, which has not been realized so far, because it requires some technical effort. Instead, PALM offers two types of radiation boundary conditions for the velocity components, which are not in conflict with the pressure solver (see [../../app/inipar/#use_cmax use_cmax], [../../app/inipar/#bc_lr bc_lr] and [../../app/inipar/#bc_ns bc_ns]). For the radiation condition, the Sommerfeld radiation equation is solved at the outflow
+At the outflow, an open boundary condition is needed to ensure that disturbances of the mean flow can exit the model domain without effecting the flow upstream. For the scalar quantities, Neumann boundary conditions are used at the outflow boundary which is the simplest way. For the velocity components, a Neumann condition would require to be considered in the solution of the Poisson equation for perturbation pressure, which has not been realized so far, because it requires some technical effort. Instead, PALM offers two types of radiation boundary conditions for the velocity components, which are not in conflict with the pressure solver (see [../../app/inipar/#bc_lr bc_lr] and [../../app/inipar/#bc_ns bc_ns]). For the radiation condition, the Sommerfeld radiation equation is solved at the outflow
 {{{
 #!Latex
@@ -376 +376 @@
 \end{align*}
 }}}
-which considers flow disturbances propagating with the mean flow and by waves. Here ''ψ'' is the transported quantity and ''∂'',,n,, is the derivative normal to the outflow boundary. In PALM, based on the equation above, the radiation boundary condition is realized in two ways as follows.
+which considers flow disturbances propagating with the mean flow and by waves. Here ''ψ'' is the transported quantity and ''∂'',,n,, is the derivative normal to the outflow boundary. In general, the phase velocity ''c'',,ψ,, is calculated as described below (''Variable Phase Velocity''). Since r4845, PALM always uses a constant phase velocity, which is assumed as the maximum velocity allowed by the CFL criterion, i.e. for a Courant number of one (see section ''Constant Phase Velocity'' further below).
 
 
@@ -441 +441 @@
 
 
-==== Constant Phase velocity ====
+==== Constant Phase velocity (used in PALM since r4845) ====
 
 Setting ''c'',,ψ,, = ''c'',,max,, leads to a more simple radiation boundary condition (here e.g. for a left-right flow along positive ''x''-direction):
@@ -450 +450 @@
 \end{align*}
 }}}
-with ''ψ = {u,v,w}''. This formulation of the radiation boundary condtions saves computational time compared to the formulation of a variable Phase velocity. Although, [#orlanski1976 Orlanski (1976)] suggested that this approach of radiation boundary condition leads to reflection for waves smaller than ''c'',,max,, which may occur in complex geophysical flows, our simulations of a convective boundary layer with background wind have been stable so far.
+with ''ψ = {u,v,w}''. This formulation of the radiation boundary condtions saves computational time compared to the formulation of a variable Phase velocity. Although, [#orlanski1976 Orlanski (1976)] suggested that this approach of radiation boundary condition leads to reflection for waves smaller than ''c'',,max,, which may occur in complex geophysical flows, our simulations of stable and convective boundary layers with background wind have shown no problems so far.