Add option for truly 2D meshes; improve documentation; add further an…

…d revamp examples

doc/examples/fluid/README.md

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+# README #
+
+This example shows how to set up 2D fluid flow in a channel around a rigid obstacle, using Taylor-Hood elements.
+
+
+### Instructions ###
+
+Run the simulation, either in one of the provided Docker containers or using your own FEniCSx/Ambit installation, using the command
+```
+mpiexec -n 1 python3 fluid_channel.py
+```
+It is fully sufficient to use one core (mpiexec -n 1) for the presented setup.
+
+Open the results file results_channel_velocity.xdmf and results_channel_pressure.xdmf in Paraview, and visualize the velocity as well as the pressure over time.
+
+### Solution
+
+The figure shows the velocity magnitude (top) as well as the pressure (bottom part) at the end of the simulation.

doc/examples/fluid/fluid_channel.py

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+#!/usr/bin/env python3
+
+"""
+A 2D fluid dynamics problem of incompressible Navier-Stokes channel flow around a rigid cylindrical obstacle.
+"""
+
+import ambit_fe
+import numpy as np
+from pathlib import Path
+
+
+def main():
+
+    basepath = str(Path(__file__).parent.absolute())
+
+    """
+    Parameters for input/output
+    """
+    IO_PARAMS           = {# problem type 'fluid': incompressible Navier-Stokes flow
+                           'problem_type'          : 'fluid',
+                           # the meshes for the domain and boundary topology are specified separately
+                           'mesh_domain'           : basepath+'/input/channel_domain.xdmf',
+                           'mesh_boundary'         : basepath+'/input/channel_boundary.xdmf',
+                           # at which step frequency to write results (set to 0 in order to not write any output)
+                           'write_results_every'   : 1,
+                           # where to write the output to
+                           'output_path'           : basepath+'/tmp/',
+                           # which results to write
+                           'results_to_write'      : ['velocity','pressure'],
+                           # the 'midfix' for all simulation result file names: will be results_<simname>_<field>.xdmf/.h5
+                           'simname'               : 'fluid_channel'}
+
+    """
+    Parameters for the linear and nonlinear solution schemes
+    """
+    SOLVER_PARAMS       = {'solve_type'            : 'direct',
+                           #'direct_solver'         : 'superlu_dist', # no idea why, but mumps does not seem to like this system in parallel...
+                           'tol_res'               : [1e-8, 1e-8],
+                           'tol_inc'               : [1e-8, 1e-8]}
+
+    """
+    Parameters for the fluid mechanics time integration scheme, plus the global time parameters
+    """
+    TIME_PARAMS         = {'maxtime'               : 0.5,
+                           'numstep'               : 100,
+                           'timint'                : 'ost',
+                           'theta_ost'             : 1.0}
+
+    """
+    Finite element parameters: Taylor-Hood elements with quadratic approximation for the velocity and linear approximation for the pressure
+    """
+    FEM_PARAMS          = {# the order of the finite element ansatz functions for the velocity and pressure
+                           'order_vel'             : 2,
+                           'order_pres'            : 1,
+                           # the degree of the quadrature scheme
+                           'quad_degree'           : 5}
+
+    """
+    Constitutive parameters for the fluid: let's use parameters of glycerine
+    """
+    MATERIALS           = { 'MAT1' : {'newtonian' : {'mu' : 1420.0e-6}, # kPa s
+                                      'inertia' : {'rho' : 1.26e-6}} }  # kg/mm^3
+
+
+    """
+    Time curves, e.g. any prescribed time-controlled/-varying loads or functions
+    """
+    class time_curves():
+
+        def tc1(self, t):
+
+            Umax = 1e3
+
+            t_ramp = 0.3
+
+            return Umax * 0.5*(1.-np.cos(np.pi*t/t_ramp)) * (t < t_ramp) + Umax * (t >= t_ramp)
+
+
+    """
+    Boundary conditions: ids: 1: inflow, 2: bottom wall, 3: axial outflow, 4: top wall - 5: obstacle
+    Wall and obstactle are fixed, in-flow velocity is prescribed, outflow is free ("Neumann zero")
+    """
+    BC_DICT           = { 'dirichlet' : [{'id' : [1], 'dir' : 'x', 'curve' : 1},
+                                         {'id' : [2,4,5], 'dir' : 'all', 'val' : 0.}]}
+
+
+    # problem setup
+    problem = ambit_fe.ambit_main.Ambit(IO_PARAMS, TIME_PARAMS, SOLVER_PARAMS, FEM_PARAMS, MATERIALS, BC_DICT, time_curves=time_curves())
+
+    # solve time-dependent problem
+    problem.solve_problem()
+
+
+
+if __name__ == "__main__":
+
+    main()