mesh_convergence

The mesh_convergence test group (compass.landice.tests.mesh_convergence.MeshConvergence) implements a suite of spatial convergence tests for MALI on planar, doubly periodic hexagonal meshes (see mesh_convergence). Here we describe the shared framework and the individual test cases.

framework

The test group shares several base classes and config/namelist/streams files that are used by all three test cases.

ConvTestCase

compass.landice.tests.mesh_convergence.conv_test_case.ConvTestCase is the shared base class for all convergence test cases. It reads the list of resolutions from [mesh_convergence] resolutions and calls _setup_steps() to construct the appropriate init and forward steps for each resolution. Each child class must implement create_init and create_analysis to supply the test-case-specific init and analysis step objects.

The configure method re-runs _setup_steps in case the user has changed the resolution list in a config file, and then calls update_cores to set the number of MPI tasks for each forward step based on the mesh size and the goal_cells_per_core / max_cells_per_core config options.

ConvInit

compass.landice.tests.mesh_convergence.conv_init.ConvInit is the shared base class for all init steps. Its run method creates a planar hexagonal mesh of the requested resolution using mpas_tools.planar_hex.make_planar_hex_mesh, culls and converts the mesh, centers it, and writes mesh.nc and graph.info. Each test case provides a child class of ConvInit that calls super().run() and then adds the appropriate initial conditions for that test.

ConvAnalysis

compass.landice.tests.mesh_convergence.conv_analysis.ConvAnalysis is the shared base class for all analysis steps. Its __init__ method registers the forward-step output files as analysis inputs using the naming convention {resolution}km_output.nc → ../{resolution}km/forward/output.nc. Each test case provides a child class that implements the run method and, typically, an rmse helper method.

Forward

compass.landice.tests.mesh_convergence.forward.Forward is shared by all test cases. It reads the common namelist.forward and streams.forward files from the mesh_convergence package, and additionally reads test-case-specific namelist/streams files if they exist in the child test-case package. The time step for each resolution is set via the get_dt_duration method to satisfy an advective CFL condition based on target_velocity and scaled proportionally to each mesh resolution.

Config / namelist / streams files

mesh_convergence.cfg sets default values for options shared across all test cases (resolutions, domain size, core counts, etc.). Each test case additionally ships its own <name>.cfg with test-specific defaults.

namelist.forward sets common MALI namelist options (e.g. third-order spatial and temporal advection schemes) and is applied first; test-case namelist files are applied on top to allow overrides.

streams.forward and streams.template define the input and output streams; the output interval is filled in by the Forward step from the computed run duration.

test cases

horizontal_advection

compass.landice.tests.mesh_convergence.horizontal_advection.HorizontalAdvection tests convergence of passive-tracer advection.

Init (compass.landice.tests.mesh_convergence.horizontal_advection.init.Init) sets up a uniform ice slab with a Gaussian blob of passiveTracer2d at the domain center plus a spatially uniform prescribed velocity (uReconstructX, uReconstructY) chosen so that the tracer completes exactly one circuit of the periodic domain in the configured run duration.

Analysis (compass.landice.tests.mesh_convergence.horizontal_advection.analysis.Analysis) computes the RMSE of passiveTracer2d between the initial and final states at each resolution, fits a power law, and saves convergence.png.

horizontal_advection_thickness

compass.landice.tests.mesh_convergence.horizontal_advection_thickness.HorizontalAdvectionThickness is structurally identical to horizontal_advection but tests convergence of ice-thickness advection instead.

Init (compass.landice.tests.mesh_convergence.horizontal_advection_thickness.init.Init) places a Gaussian bump of ice thickness on top of a uniform background layer, with the same prescribed velocity approach as the tracer test.

Analysis (compass.landice.tests.mesh_convergence.horizontal_advection_thickness.analysis.Analysis) computes the RMSE of thickness between the initial and final states.

halfar

compass.landice.tests.mesh_convergence.halfar.Halfar tests convergence of the ice-dynamics solver by comparing against the Halfar analytic similarity solution.

Init (compass.landice.tests.mesh_convergence.halfar.init.Init) calls compass.landice.tests.dome.setup_mesh.setup_dome_initial_conditions() to create the Halfar dome initial condition on the planar hexagonal mesh.

Analysis (compass.landice.tests.mesh_convergence.halfar.analysis.Analysis) computes two error metrics:

The RMSE between simulated and analytic Halfar thickness over all cells that contain ice in either solution (convergence_rmse.png).
The absolute error at the dome center (convergence_dome.png).

The order of convergence is derived from the RMSE metric and compared against conv_thresh (fail below) and conv_max (warn above) config options.