Merge pull request #122 from thetisproject/than_tracer

Adding 2-D tracer transport in thetis

test/tracerEq/test_consistency_2d.py

@@ -0,0 +1,128 @@
+# Tracer box in 2D
+# ================
+#
+# Solves a standing wave in a rectangular basin using wave equation.
+#
+# This version uses a constant tracer to check local/global conservation of tracers.
+#
+# Initial condition for elevation corresponds to a standing wave.
+# Time step and export interval are chosen based on theorethical
+# oscillation frequency. Initial condition repeats every 20 exports.
+#
+#
+# Thanasis Angeloudis based on Tuomas Karna test_consistency.py 15-01-2018
+
+from thetis import *
+
+def run_tracer_consistency(constant_c = True, **model_options):
+
+    t_cycle = 2000.0  # standing wave period
+    depth = 50.0  # average depth
+    lx = np.sqrt(9.81*depth)*t_cycle  # wave length
+    ly = 3000.0
+    nx = 18
+    ny = 2
+    mesh2d = RectangleMesh(nx, ny, lx, ly)
+    tracer_value = 4.5
+    elev_amp = 2.0
+    # estimate of max advective velocity used to estimate time step
+    u_mag = Constant(1.0)
+
+    outputdir = 'outputs'
+
+    # bathymetry
+    p1_2d = FunctionSpace(mesh2d, 'CG', 1)
+    bathymetry_2d = Function(p1_2d, name='Bathymetry')
+    x_2d, y_2d = SpatialCoordinate(mesh2d)
+    # non-trivial bathymetry, to properly test 2d tracer conservation
+    bathymetry_2d.interpolate(depth + depth/10.*sin(x_2d/lx*pi))
+
+
+    # set time step, export interval and run duration
+    n_steps = 8
+    t_export = round(float(t_cycle/n_steps))
+    # for testing tracer conservation, we don't want to come back to the initial condition
+    t_end = 2.5*t_cycle
+
+    # create solver
+    solver_obj = solver2d.FlowSolver2d(mesh2d, bathymetry_2d)
+    options = solver_obj.options
+    options.use_nonlinear_equations = True
+    options.solve_tracer = True
+    options.use_limiter_for_tracers = not constant_c
+    options.simulation_export_time = t_export
+    options.simulation_end_time = t_end
+    options.horizontal_velocity_scale = Constant(u_mag)
+    options.check_volume_conservation_2d = True
+    options.check_tracer_conservation = True
+    options.check_tracer_overshoot = True
+    options.timestepper_type = 'CrankNicolson'
+    options.output_directory = outputdir
+    options.fields_to_export = ['uv_2d', 'elev_2d', 'tracer_2d']
+    options.update(model_options)
+
+    if not options.no_exports:
+        print_output('Exporting to {:}'.format(options.output_directory))
+
+    solver_obj.create_function_spaces()
+    elev_init = Function(solver_obj.function_spaces.H_2d)
+    elev_init.project(-elev_amp*cos(2*pi*x_2d/lx))
+
+    tracer_init2d = None
+    if options.solve_tracer and constant_c:
+        tracer_init2d = Function(solver_obj.function_spaces.Q_2d, name='initial tracer')
+        tracer_init2d.assign(tracer_value)
+    if options.solve_tracer and not constant_c:
+        tracer_init2d = Function(solver_obj.function_spaces.Q_2d, name='initial tracer')
+        tracer_l = 0
+        tracer_r = 30.0
+        tracer_init2d.interpolate(tracer_l + (tracer_r - tracer_l)*0.5*(1.0 + sign(x_2d - lx/4)))
+
+    solver_obj.assign_initial_conditions(elev=elev_init, tracer=tracer_init2d )
+    solver_obj.iterate()
+
+    # TODO do these checks every export ...
+    vol2d, vol2d_rerr = solver_obj.callbacks['export']['volume2d']()
+    assert vol2d_rerr < 1e-10, '2D volume is not conserved'
+    if options.solve_tracer:
+        tracer_int, tracer_int_rerr = solver_obj.callbacks['export']['tracer_2d mass']()
+        assert abs(tracer_int_rerr) < 1e-4, 'tracer is not conserved'
+        smin, smax, undershoot, overshoot = solver_obj.callbacks['export']['tracer_2d overshoot']()
+        max_abs_overshoot = max(abs(undershoot), abs(overshoot))
+        overshoot_tol = 1e-12
+        msg = 'Tracer overshoots are too large: {:}'.format(max_abs_overshoot)
+        assert max_abs_overshoot < overshoot_tol, msg
+
+
+
+def test_const_tracer():
+    """
+    Test CrankNicolson timeintegrator without slope limiters
+    Constant tracer, should remain constant
+    """
+    run_tracer_consistency(constant_c= True,
+                           use_nonlinear_equations=True,
+                           solve_tracer=True,
+                           use_limiter_for_tracers=False,
+                           no_exports=True)
+
+
+
+def test_nonconst_tracer():
+    """
+    Test CrankNicolson timeintegrator  with slope limiters
+    Non-trivial tracer, should see no overshoots and be conserved
+    """
+    run_tracer_consistency(constant_c= False,
+                           use_nonlinear_equations=True,
+                           solve_tracer=True,
+                           use_limiter_for_tracers=True,
+                           no_exports=True)
+
+
+if __name__ == '__main__':
+    run_tracer_consistency(constant_c= False,
+                           use_nonlinear_equations=True,
+                           solve_tracer=True,
+                           use_limiter_for_tracers=False,
+                           no_exports=False)

test/tracerEq/test_h-advection_mes.py

@@ -120,7 +120,7 @@ def export_func():
             next_export_t += solverobj.options.simulation_export_time
             iexport += 1
 
-    # project analytical solultion on high order mesh
+    # project analytical solution on high order mesh
     t_const.assign(t)
     salt_ana_ho.project(ana_salt_expr)
     # compute L2 norm

test/tracerEq/test_h-advection_mes_2d.py

@@ -0,0 +1,198 @@
+"""
+Testing 2D horizontal advection of tracers
+
+Tuomas Karna, edited by Athanasios Angeloudis
+"""
+from thetis import *
+import numpy
+from scipy import stats
+import pytest
+
+
+def run(refinement, **model_options):
+    print_output('--- running refinement {:}'.format(refinement))
+
+    # domain dimensions - channel in x-direction
+    lx = 15.0e3
+    ly = 6.0e3/refinement
+    area = lx*ly
+    depth = 40.0
+    u = 1.0
+
+    # mesh
+    nx = 6*refinement + 1
+    ny = 1  # constant -- channel
+    mesh2d = RectangleMesh(nx, ny, lx, ly)
+
+    # simulation run time
+    t_end = 3000.0
+    # initial time
+    t_init = 0.0
+    t_export = (t_end - t_init)/8.0
+
+    # outputs
+    outputdir = 'outputs'
+
+    # bathymetry
+    P1_2d = FunctionSpace(mesh2d, 'CG', 1)
+    bathymetry_2d = Function(P1_2d, name='Bathymetry')
+    bathymetry_2d.assign(depth)
+
+    solverobj = solver2d.FlowSolver2d(mesh2d, bathymetry_2d)
+    options = solverobj.options
+    options.use_nonlinear_equations = False
+    options.use_lax_friedrichs_velocity = True
+    options.lax_friedrichs_velocity_scaling_factor = Constant(1.0)
+    options.use_lax_friedrichs_tracer = False
+    options.horizontal_velocity_scale = Constant(abs(u))
+    options.no_exports = True
+    options.output_directory = outputdir
+    options.simulation_end_time = t_end
+    options.simulation_export_time = t_export
+    options.solve_tracer = True
+    options.use_limiter_for_tracers = True
+    options.fields_to_export = ['tracer_2d']
+    options.update(model_options)
+    uv_expr = as_vector((u, 0))
+    bnd_salt_2d = {'value': Constant(0.0), 'uv': uv_expr}
+    bnd_uv_2d = {'uv': uv_expr}
+    solverobj.bnd_functions['tracer'] = {
+        1: bnd_salt_2d,
+        2: bnd_salt_2d,
+    }
+    solverobj.bnd_functions['momentum'] = {
+        1: bnd_uv_2d,
+        2: bnd_uv_2d,
+    }
+
+    solverobj.create_equations()
+
+    t = t_init  # simulation time
+
+    x0 = 0.3*lx
+    sigma = 1600.
+    xy = SpatialCoordinate(solverobj.mesh2d)
+    t_const = Constant(t)
+    ana_tracer_expr = exp(-(xy[0] - x0 - u*t_const)**2/sigma**2)
+    tracer_ana = Function(solverobj.function_spaces.H_2d, name='tracer analytical')
+    uv_init = Function(solverobj.function_spaces.U_2d, name='initial uv')
+    uv_init.project(uv_expr)
+    solverobj.assign_initial_conditions(uv=uv_init, tracer=ana_tracer_expr)
+
+    # export analytical solution
+    if not options.no_exports:
+        out_tracer_ana = File(os.path.join(options.output_directory, 'tracer_ana.pvd'))
+
+    def export_func():
+        if not options.no_exports:
+            solverobj.export()
+            # update analytical solution to correct time
+            t_const.assign(t)
+            out_tracer_ana.write(tracer_ana.project(ana_tracer_expr))
+
+    # export initial conditions
+    export_func()
+
+    # custom time loop that solves tracer equation only
+    ti = solverobj.timestepper.timesteppers.tracer
+
+    i = 0
+    iexport = 1
+    next_export_t = t + solverobj.options.simulation_export_time
+    while t < t_end - 1e-8:
+        ti.advance(t)
+        t += solverobj.dt
+        i += 1
+        if t >= next_export_t - 1e-8:
+            print_output('{:3d} i={:5d} t={:8.2f} s salt={:8.2f}'.format(iexport, i, t, norm(solverobj.fields.tracer_2d)))
+            export_func()
+            next_export_t += solverobj.options.simulation_export_time
+            iexport += 1
+
+    # project analytical solution on high order mesh
+    t_const.assign(t)
+
+    # compute L2 norm
+    l2_err = errornorm(ana_tracer_expr, solverobj.fields.tracer_2d)/numpy.sqrt(area)
+    print_output('L2 error {:.12f}'.format(l2_err))
+
+    return l2_err
+
+
+def run_convergence(ref_list, saveplot=False, **options):
+    """Runs test for a list of refinements and computes error convergence rate"""
+
+    polynomial_degree = options.get('polynomial_degree', 1)
+    l2_err = []
+    for r in ref_list:
+        l2_err.append(run(r, **options))
+    x_log = numpy.log10(numpy.array(ref_list, dtype=float)**-1)
+    y_log = numpy.log10(numpy.array(l2_err))
+    setup_name = 'h-diffusion'
+
+    def check_convergence(x_log, y_log, expected_slope, field_str, saveplot):
+        slope_rtol = 0.20
+        slope, intercept, r_value, p_value, std_err = stats.linregress(x_log, y_log)
+        if saveplot:
+            import matplotlib.pyplot as plt
+            fig, ax = plt.subplots(figsize=(5, 5))
+            # plot points
+            ax.plot(x_log, y_log, 'k.')
+            x_min = x_log.min()
+            x_max = x_log.max()
+            offset = 0.05*(x_max - x_min)
+            npoints = 50
+            xx = numpy.linspace(x_min - offset, x_max + offset, npoints)
+            yy = intercept + slope*xx
+            # plot line
+            ax.plot(xx, yy, linestyle='--', linewidth=0.5, color='k')
+            ax.text(xx[2*int(npoints/3)], yy[2*int(npoints/3)], '{:4.2f}'.format(slope),
+                    verticalalignment='top',
+                    horizontalalignment='left')
+            ax.set_xlabel('log10(dx)')
+            ax.set_ylabel('log10(L2 error)')
+            ax.set_title(' '.join([setup_name, field_str, 'degree={:}'.format(polynomial_degree)]))
+            ref_str = 'ref-' + '-'.join([str(r) for r in ref_list])
+            degree_str = 'o{:}'.format(polynomial_degree)
+            imgfile = '_'.join(['convergence', setup_name, field_str, ref_str, degree_str])
+            imgfile += '.png'
+            imgdir = create_directory('plots')
+            imgfile = os.path.join(imgdir, imgfile)
+            print_output('saving figure {:}'.format(imgfile))
+            plt.savefig(imgfile, dpi=200, bbox_inches='tight')
+        if expected_slope is not None:
+            err_msg = '{:}: Wrong convergence rate {:.4f}, expected {:.4f}'.format(setup_name, slope, expected_slope)
+            assert slope > expected_slope*(1 - slope_rtol), err_msg
+            print_output('{:}: convergence rate {:.4f} PASSED'.format(setup_name, slope))
+        else:
+            print_output('{:}: {:} convergence rate {:.4f}'.format(setup_name, field_str, slope))
+        return slope
+
+    check_convergence(x_log, y_log, polynomial_degree+1, 'tracer', saveplot)
+
+# ---------------------------
+# standard tests for pytest
+# ---------------------------
+
+
+@pytest.fixture(params=[1])
+def polynomial_degree(request):
+    return request.param
+
+
+@pytest.mark.parametrize(('stepper'),
+                         [('CrankNicolson')])
+
+def test_horizontal_advection(polynomial_degree, stepper, ):
+    run_convergence([1, 2, 3], polynomial_degree=polynomial_degree,
+                    timestepper_type=stepper)
+
+# ---------------------------
+# run individual setup for debugging
+# ---------------------------
+
+
+if __name__ == '__main__':
+    run_convergence([1, 2, 3, 4], polynomial_degree=1,
+                    timestepper_type='CrankNicolson',
+                    no_exports=False, saveplot=True)