.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/imod-wq/Elder.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:here  to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_imod-wq_Elder.py: Elder ===== The classic 2D Elder problem demonstrates free convection. Traditionally this was created for heat transport, but we use a modified version for salt transport. The conceptual model can be seen as a 2D sand box, with on top a salt lake in the center and fresh lakes on both the outer edges of the top row. More info about the theory behind the Elder problem: Simpson, J., & Clement, P. (2003). Theoretical analysis of the worthiness of Henry and Elder problems as benchmark of density-dependent groundwater flow models. Advances in Water Resources, 1708 (02). Retrieved from http://www.eng.auburn.edu/~clemept/publsihed_pdf/awrmat.pdf .. GENERATED FROM PYTHON SOURCE LINES 22-23 We'll start with the usual imports .. GENERATED FROM PYTHON SOURCE LINES 23-30 .. code-block:: default import matplotlib.pyplot as plt import numpy as np import xarray as xr import imod .. GENERATED FROM PYTHON SOURCE LINES 31-37 Discretization -------------- We'll start off by creating a model discretization, since this is a simple conceptual model. The model is a 2D cross-section, hence nrow = 1. .. GENERATED FROM PYTHON SOURCE LINES 37-46 .. code-block:: default nrow = 1 ncol = 160 nlay = 82 dz = 1.875 dx = 3.75 dy = -dx .. GENERATED FROM PYTHON SOURCE LINES 47-48 setup tops and bottoms .. GENERATED FROM PYTHON SOURCE LINES 48-56 .. code-block:: default top1D = xr.DataArray( np.arange(nlay * dz, 0.0, -dz), {"layer": np.arange(1, nlay + 1)}, ("layer") ) bot = top1D - dz top = nlay * dz .. GENERATED FROM PYTHON SOURCE LINES 57-58 Set up ibound, which sets where active cells are (ibound = 1.0) .. GENERATED FROM PYTHON SOURCE LINES 58-73 .. code-block:: default bnd = xr.DataArray( data=np.full((nlay, nrow, ncol), 1.0), coords={ "y": [0.5], "x": np.arange(0.5 * dx, dx * ncol, dx), "layer": np.arange(1, 1 + nlay), "dx": dx, "dy": dy, }, dims=("layer", "y", "x"), ) fig, ax = plt.subplots() bnd.plot(y="layer", yincrease=False, ax=ax) .. image-sg:: /examples/imod-wq/images/sphx_glr_Elder_001.png :alt: y = 0.5, dx = 3.75, dy = -3.75 :srcset: /examples/imod-wq/images/sphx_glr_Elder_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 74-79 Boundary Conditions ------------------- Set the constant heads by specifying a negative value in iboud, that is: bnd[index] = -1 .. GENERATED FROM PYTHON SOURCE LINES 79-88 .. code-block:: default bnd[0, :, 0:40] = 0 bnd[0, :, 121:160] = 0 bnd[1, :, 0] = -1 bnd[1, :, 159] = -1 fig, ax = plt.subplots() bnd.plot(y="layer", yincrease=False, ax=ax) .. image-sg:: /examples/imod-wq/images/sphx_glr_Elder_002.png :alt: y = 0.5, dx = 3.75, dy = -3.75 :srcset: /examples/imod-wq/images/sphx_glr_Elder_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 89-91 Define the icbund, which sets which cells in the solute transport model are active, inactive or constant. .. GENERATED FROM PYTHON SOURCE LINES 91-107 .. code-block:: default icbund = xr.DataArray( data=np.full((nlay, nrow, ncol), 1.0), coords={ "y": [0.5], "x": np.arange(0.5 * dx, dx * ncol, dx), "layer": np.arange(1, nlay + 1), }, dims=("layer", "y", "x"), ) icbund[81, :, :] = -1 icbund[0, :, 41:120] = -1 fig, ax = plt.subplots() icbund.plot(y="layer", yincrease=False, ax=ax) .. image-sg:: /examples/imod-wq/images/sphx_glr_Elder_003.png :alt: y = 0.5 :srcset: /examples/imod-wq/images/sphx_glr_Elder_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 108-112 Initial Conditions ------------------ Define the starting concentration .. GENERATED FROM PYTHON SOURCE LINES 112-129 .. code-block:: default sconc = xr.DataArray( data=np.full((nlay, nrow, ncol), 0.0), coords={ "y": [0.5], "x": np.arange(0.5 * dx, dx * ncol, dx), "layer": np.arange(1, nlay + 1), }, dims=("layer", "y", "x"), ) sconc[81, :, :] = 0 sconc[0, :, 41:120] = 280.0 fig, ax = plt.subplots() sconc.plot(y="layer", yincrease=False, ax=ax) .. image-sg:: /examples/imod-wq/images/sphx_glr_Elder_004.png :alt: y = 0.5 :srcset: /examples/imod-wq/images/sphx_glr_Elder_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 130-134 Build ----- Finally, we build the model. .. GENERATED FROM PYTHON SOURCE LINES 134-160 .. code-block:: default m = imod.wq.SeawatModel("Elder") m["bas"] = imod.wq.BasicFlow(ibound=bnd, top=top, bottom=bot, starting_head=0.0) m["lpf"] = imod.wq.LayerPropertyFlow( k_horizontal=0.411, k_vertical=0.411, specific_storage=0.0 ) m["btn"] = imod.wq.BasicTransport( icbund=icbund, starting_concentration=sconc, porosity=0.1 ) m["adv"] = imod.wq.AdvectionTVD(courant=1.0) m["dsp"] = imod.wq.Dispersion(longitudinal=0.0, diffusion_coefficient=0.308) m["vdf"] = imod.wq.VariableDensityFlow(density_concentration_slope=0.71) m["wel"] = imod.wq.Well(id_name="wel", x=0.5 * dx, y=0.5, rate=0.28512) m["pcg"] = imod.wq.PreconditionedConjugateGradientSolver( max_iter=150, inner_iter=30, hclose=0.0001, rclose=0.1, relax=0.98, damp=1.0 ) m["gcg"] = imod.wq.GeneralizedConjugateGradientSolver( max_iter=150, inner_iter=30, cclose=1.0e-6, preconditioner="mic", lump_dispersion=True, ) m["oc"] = imod.wq.OutputControl(save_head_idf=True, save_concentration_idf=True) m.create_time_discretization(additional_times=["2000-01-01T00:00", "2020-01-01T00:00"]) .. GENERATED FROM PYTHON SOURCE LINES 161-162 Now we write the model .. GENERATED FROM PYTHON SOURCE LINES 162-166 .. code-block:: default modeldir = imod.util.temporary_directory() m.write(modeldir, resultdir_is_workdir=True) .. GENERATED FROM PYTHON SOURCE LINES 167-185 Run --- You can run the model using the comand prompt and the iMOD-WQ executable. This is part of the iMOD v5 release, which can be downloaded here: https://oss.deltares.nl/web/imod/download-imod5 . This only works on Windows. To run your model, open up a command prompt and run the following commands: .. code-block:: batch cd c:\path\to\modeldir c:\path\to\imod\folder\iMOD-WQ_V5_3_SVN359_X64R.exe Elder.run Note that the version name of your executable might differ. .. GENERATED FROM PYTHON SOURCE LINES 187-205 Visualise results ----------------- After succesfully running the model, you can plot results as follows: .. code:: python head = imod.idf.open(modeldir / "results/head/*.idf") fig, ax = plt.subplots() head.plot(yincrease=False, ax=ax) conc = imod.idf.open(modeldir / "results/conc/*.idf") fig, ax = plt.subplots() conc.plot(levels=range(0, 35, 5), yincrease=False, ax=ax) .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 1.344 seconds) .. _sphx_glr_download_examples_imod-wq_Elder.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:Download Python source code: Elder.py  .. container:: sphx-glr-download sphx-glr-download-jupyter :download:Download Jupyter notebook: Elder.ipynb  .. only:: html .. rst-class:: sphx-glr-signature Gallery generated by Sphinx-Gallery `_