""" Elder ===== The classic 2D Elder problem demonstrates free convection. Traditionally this was created for heat transport, but we use a modified version for salt tranpsort. 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 """ # %% # We'll start with the usual imports import matplotlib.pyplot as plt import numpy as np import xarray as xr import imod # %% # 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. nrow = 1 ncol = 160 nlay = 82 dz = 1.875 dx = 3.75 dy = -dx # %% # setup tops and bottoms top1D = xr.DataArray( np.arange(nlay * dz, 0.0, -dz), {"layer": np.arange(1, nlay + 1)}, ("layer") ) bot = top1D - dz top = nlay * dz # %% # Set up ibound, which sets where active cells are (ibound = 1.0) 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) # %% # Boundary Conditions # ------------------- # # Set the constant heads by specifying a negative value in iboud, # that is: bnd[index] = -1` 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) # %% # Define the icbund, which sets which cells # in the solute transport model are active, inactive or constant. 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) # %% # Initial Conditions # ------------------ # # Define the starting concentration 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) # %% # Build # ----- # # Finally, we build the model. 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"]) # %% # Now we write the model modeldir = imod.util.temporary_directory() m.write(modeldir, resultdir_is_workdir=True) # %% # 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. # # %% # 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) # # %%