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Forest Model | ||
-------------- | ||
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The forest model provides an option to include the drag from forested regions to be included in the momentum equation. The | ||
drag force is calculated as follows: | ||
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.. math:: | ||
F_i= - C_d L(x,y,z) U_i | U_i | | ||
Here :math:`C_d` is the coefficient of drag for the forested region and :math:`L(x,y,z)` is the leaf area density (LAD) for the | ||
forested region. A three-dimensional model for the LAD is usually unavailable and is also cumbersome to use if there are thousands | ||
of trees. Two different models are available as an alternative: | ||
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.. math:: | ||
L=\frac{LAI}{h} | ||
.. math:: | ||
L(z)=L_m \left(\frac{h - z_m}{h - z}\right)^n exp\left[n \left(1 -\frac{h - z_m}{h - z}\right )\right] | ||
Here :math:`LAI` is the leaf area index and is available from measurements, :math:`h` is the height of the tree, :math:`z_m` is the location | ||
of the maximum LAD, :math:`L_m` is the maximum value of LAD at :math:`z_m` and :math:`n` is a model constant with values 6 (below :math:`z_m`) and 0.5 | ||
(above :math:`z_m`), respectively. :math:`L_m` is computed by integrating the following equation (see `Lalic and Mihailovic (2004) | ||
<https://doi.org/10.1175/1520-0450(2004)043<0641:AERDLD>2.0.CO;2>`_): | ||
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.. math:: | ||
LAI = \int_{0}^{h} L(z) dz | ||
The simplified model with uniform LAD is recommended for forested regions with no knowledge of the individual trees. LAI values can be used from | ||
climate model look-up tables for different regions around the world if no local remote sensing data is available. |
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1 1024 512 45 200 0.2 6 0.8 | ||
1 1024 1024 35 200 0.2 6 0.8 | ||
1 1024 1224 75 200 0.2 6 0.8 | ||
2 1024 1524 120 200 0.2 10 0.8 |
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# ------------------ INPUTS TO MAIN PROGRAM ------------------- | ||
max_step = 50 | ||
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amrex.fpe_trap_invalid = 1 | ||
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fabarray.mfiter_tile_size = 1024 1024 1024 | ||
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# PROBLEM SIZE & GEOMETRY | ||
geometry.prob_extent = 2048 2048 1024 | ||
amr.n_cell = 64 64 32 | ||
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geometry.is_periodic = 1 1 0 | ||
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zlo.type = "SlipWall" | ||
zhi.type = "SlipWall" | ||
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# TIME STEP CONTROL | ||
erf.fixed_dt = 2.0 # fixed time step depending on grid resolution | ||
erf.cfl = 0.5 | ||
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# DIAGNOSTICS & VERBOSITY | ||
erf.sum_interval = 1 # timesteps between computing mass | ||
erf.v = 1 # verbosity in ERF.cpp | ||
amr.v = 1 # verbosity in Amr.cpp | ||
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# REFINEMENT / REGRIDDING | ||
amr.max_level = 0 # maximum level number allowed | ||
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# CHECKPOINT FILES | ||
erf.check_file = chk # root name of checkpoint file | ||
erf.check_int = 50 # number of timesteps between checkpoints | ||
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# PLOTFILES | ||
erf.plot_file_1 = plt # prefix of plotfile name | ||
erf.plot_int_1 = 50 # number of timesteps between plotfiles | ||
erf.plot_vars_1 = density rhoadv_0 x_velocity y_velocity z_velocity pressure temp theta | ||
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# SOLVER CHOICE | ||
erf.alpha_T = 0.0 | ||
erf.alpha_C = 1.0 | ||
erf.use_gravity = false | ||
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erf.molec_diff_type = "None" | ||
erf.les_type = "Smagorinsky" | ||
erf.Cs = 0.1 | ||
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erf.init_type = "uniform" | ||
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#erf.forest_file = erf_forest_def | ||
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# PROBLEM PARAMETERS | ||
prob.rho_0 = 1.0 | ||
prob.A_0 = 1.0 | ||
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prob.U_0 = 10.0 | ||
prob.V_0 = 0.0 | ||
prob.W_0 = 0.0 | ||
prob.T_0 = 300.0 | ||
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# Higher values of perturbations lead to instability | ||
# Instability seems to be coming from BC | ||
prob.U_0_Pert_Mag = 0.08 | ||
prob.V_0_Pert_Mag = 0.08 # | ||
prob.W_0_Pert_Mag = 0.0 |
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