Changes between Version 22 and Version 23 of doc/tec/noncyclic
- Timestamp:
- Feb 22, 2021 4:48:11 PM (4 years ago)
Legend:
- Unmodified
- Added
- Removed
- Modified
-
doc/tec/noncyclic
v22 v23 1 1 = Non-cyclic lateral boundary conditions = 2 2 3 Figure 1 shows the grid structure for non-cyclic boundary conditions at the left/right boundary '''LB/RB''' ([../../app/ini par/#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]).3 Figure 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]). 4 4 The indices (i,j,k) represent the directions (x,y,z). 5 5 The 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. … … 20 20 In case of a Dirichlet condition, the values at i = 0 (j = 0) are taken from i = -1 (j = -1). 21 21 In 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/ini par/#psolver psolver] has to be set to '' 'multigrid' '' because the default FFT-solver can only be applied for cyclic boundary conditions. \\\\22 For 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. \\\\ 23 23 24 24 === Inflow boundary === … … 30 30 }}} 31 31 t 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/ini par/#initializing_actions initializing_actions]).32 The quantities at the inflow are set by the initial vertical profiles (see [../../app/initialization_parameters/#initializing_actions initializing_actions]). 33 33 A Neumann condition is used for the subgrid-scale turbulent kinetic energy e (here e.g. for a left-right flow): 34 34 {{{ … … 51 51 \end{cases} . \quad (4)$ 52 52 }}} 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/ini par/#pt_damping_factor pt_damping_factor] and [../../app/inipar/#pt_damping_width pt_damping_width], respectively.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/initialization_parameters/#pt_damping_factor pt_damping_factor] and [../../app/initialization_parameters/#pt_damping_width pt_damping_width], respectively. 54 54 Both 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. 55 55 So 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/ini par/#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.56 In 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. 57 57 58 58 === Outflow boundary === … … 61 61 For the scalar quantities, Neumann boundary conditions are used at the outflow boundary which is the simplest way. 62 62 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. 63 Instead, PALM offers a radiation boundary conditions for the velocity components, which are not in conflict with the pressure solver (see [../../app/ini par/#bc_lr bc_lr] and [../../app/inipar/#bc_ns bc_ns]).63 Instead, 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]). 64 64 For the radiation condition, the Sommerfeld radiation equation is solved at the outflow 65 65 {{{ … … 146 146 147 147 PALM offers the possibility of a mass flux correction at the outflow (e.g. Tian, 2004). 148 If parameter [../../app/ini par/#conserve_volume_flow conserve_volume_flow] is set true, the mass flux at the inflow and outflow is calculated by:148 If parameter [../../app/initialization_parameters/#conserve_volume_flow conserve_volume_flow] is set true, the mass flux at the inflow and outflow is calculated by: 149 149 {{{ 150 150 #!Latex 151 151 $\dot{m} = \sum_{k=1}^{nz-1} \Delta z(k) \sum_{l=0}^{nx_i} \psi(l,k) \Delta x_i \; . \quad (12)$ 152 152 }}} 153 where Δx,,i,, and ψ is equal to Δy (Δx) and u (v) in case of [../../app/ini par/#bc_lr bc_lr] ([../../app/inipar/#bc_ns bc_ns]).153 where 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]). 154 154 The correction factor for the outflow velocity, which is necessary due to different mass fluxes at inflow and outflow, can be calculated by 155 155 {{{