Changes between Version 22 and Version 23 of doc/tec/noncyclic


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Timestamp:
Feb 22, 2021 4:48:11 PM (4 years ago)
Author:
wagner
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  • doc/tec/noncyclic

    v22 v23  
    11= Non-cyclic lateral boundary conditions =
    22
    3 Figure 1 shows the grid structure for non-cyclic boundary conditions at the left/right boundary '''LB/RB''' ([../../app/inipar/#bc_lr bc_lr]) and figure 2 for non-cyclic boundary conditions at the north/south boundary '''NB/SB''' ([../../app/inipar/#bc_ns bc_ns]).
     3Figure 1 shows the grid structure for non-cyclic boundary conditions at the left/right boundary '''LB/RB''' ([../../app/initialization_parameters/#bc_lr bc_lr]) and figure 2 for non-cyclic boundary conditions at the north/south boundary '''NB/SB''' ([../../app/initialization_parameters/#bc_ns bc_ns]).
    44The indices (i,j,k) represent the directions (x,y,z).
    55The model domain extends from -1:nx+1 in the x-direction, from -1:ny+1 in the y-direction and from 0:nzt+1 in the z-direction.
     
    2020In case of a Dirichlet condition, the values at i = 0 (j = 0) are taken from i = -1 (j = -1).
    2121In case of a radiation boundary condition, the solution of the Sommerfeld equation overwrites the prognostic values at i = 0 (j = 0). \\
    22 For non-cyclic lateral boundary conditions, the parameter [../../app/inipar/#psolver psolver] has to be set to '' 'multigrid' '' because the default FFT-solver can only be applied for cyclic boundary conditions. \\\\
     22For non-cyclic lateral boundary conditions, the parameter [../../app/initialization_parameters/#psolver psolver] has to be set to '' 'multigrid' '' because the default FFT-solver can only be applied for cyclic boundary conditions. \\\\
    2323
    2424=== Inflow boundary ===
     
    3030 }}}
    3131t denotes the time, Δt the time step and s,,init,, the initialization profile of the scalar quantities which is constant in time.
    32 The quantities at the inflow are set by the initial vertical profiles (see [../../app/inipar/#initializing_actions initializing_actions]).
     32The quantities at the inflow are set by the initial vertical profiles (see [../../app/initialization_parameters/#initializing_actions initializing_actions]).
    3333A Neumann condition is used for the subgrid-scale turbulent kinetic energy e (here e.g. for a left-right flow):
    3434{{{
     
    5151\end{cases} . \quad (4)$
    5252 }}}
    53 d,,f,, is a damping factor to control the damping intensity, and d,,w,, is the width of the relaxation region extending from the inflow. Quantities d,,f,, and d,,w,, can be set with parameters [../../app/inipar/#pt_damping_factor pt_damping_factor] and [../../app/inipar/#pt_damping_width pt_damping_width], respectively.
     53d,,f,, is a damping factor to control the damping intensity, and d,,w,, is the width of the relaxation region extending from the inflow. Quantities d,,f,, and d,,w,, can be set with parameters [../../app/initialization_parameters/#pt_damping_factor pt_damping_factor] and [../../app/initialization_parameters/#pt_damping_width pt_damping_width], respectively.
    5454Both parameters have to be set by the user and must be adjusted case-by-case, because both parameters depend on the numerical and physical conditions, so that application of universal default values is not possible.
    5555So far, we have experience with gravity waves in case of cold air outbreaks, which grow in amplitude up to quite extreme values, if no damping is applied.
    56 In the respective simulations, we used typical values for [../../app/inipar/#pt_damping_factor pt_damping_factor] of 0.05 and for [../../app/inipar/#pt_damping_width pt_damping_width] of 25 km in order to prevent the gravity waves from growing.
     56In the respective simulations, we used typical values for [../../app/initialization_parameters/#pt_damping_factor pt_damping_factor] of 0.05 and for [../../app/initialization_parameters/#pt_damping_width pt_damping_width] of 25 km in order to prevent the gravity waves from growing.
    5757
    5858=== Outflow boundary ===
     
    6161For the scalar quantities, Neumann boundary conditions are used at the outflow boundary which is the simplest way.
    6262For 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.
    63 Instead, PALM offers a 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]).
     63Instead, PALM offers a radiation boundary conditions for the velocity components, which are not in conflict with the pressure solver (see [../../app/initialization_parameters/#bc_lr bc_lr] and [../../app/initialization_parameters/#bc_ns bc_ns]).
    6464For the radiation condition, the Sommerfeld radiation equation is solved at the outflow
    6565{{{
     
    146146
    147147PALM offers the possibility of a mass flux correction at the outflow (e.g. Tian, 2004).
    148 If parameter [../../app/inipar/#conserve_volume_flow conserve_volume_flow] is set true, the mass flux at the inflow and outflow is calculated by:
     148If parameter [../../app/initialization_parameters/#conserve_volume_flow conserve_volume_flow] is set true, the mass flux at the inflow and outflow is calculated by:
    149149{{{
    150150#!Latex
    151151$\dot{m} = \sum_{k=1}^{nz-1} \Delta z(k) \sum_{l=0}^{nx_i} \psi(l,k) \Delta x_i \; . \quad (12)$
    152152}}}
    153 where Δx,,i,, and ψ is equal to Δy (Δx) and u (v) in case of [../../app/inipar/#bc_lr bc_lr] ([../../app/inipar/#bc_ns bc_ns]).
     153where Δx,,i,, and ψ is equal to Δy (Δx) and u (v) in case of [../../app/initialization_parameters/#bc_lr bc_lr] ([../../app/initialization_parameters/#bc_ns bc_ns]).
    154154The correction factor for the outflow velocity, which is necessary due to different mass fluxes at inflow and outflow, can be calculated by
    155155{{{