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Create incompressible_viscous solver and lid-driven cavity test problem (#138)
Needed to change a few things in incompressible/simulation.py as well: Neumann BC's on phi in the case of dirichlet BC's on v (and apply phi-specific BC's in the multigrid solves) Allow user-defined BC's Allow another method for the velocity update in the evolve loop The latter two are then redefined in incompressible_viscous/simulation.py. The rest of the methods are inherited from the base class. For the lid-driven cavity problem, the only free parameter is the viscosity. Since the velocity and length scales are =1, the Reynolds number is just 1/viscosity.
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‎.gitignore‎

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__pycache__/
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.DS_Store
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pyro/_version.py
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pyro.egg-info/
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pyro_hydro.egg-info/
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.eggs/

‎README.md‎

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projection method for the incompressible equations of
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hydrodynamics.
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- `incompressible_viscous`: an extension of the incompressible solver
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including a diffusion term for viscosity.
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- `lm_atm`: a solver for the equations of low Mach number
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hydrodynamics for atmospheric flows.
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‎docs/source/cavity_Re100.png‎

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‎docs/source/cavity_Re1000.png‎

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‎docs/source/cavity_Re400.png‎

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‎docs/source/incomp_viscous_converge.png‎

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‎docs/source/incompressible_viscous_basics.rst‎

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Incompressible viscous hydrodynamics solver
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===========================================
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pyro's incompressible viscous solver solves:
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.. math::
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\frac{\partial U}{\partial t} + U \cdot \nabla U + \nabla p &= \nu \nabla^2 U \\
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\nabla \cdot U &= 0
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This solver is based on pyro's incompressible solver, but modifies the
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velocity update step to take viscosity into account.
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The main parameters that affect this solver are:
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.. include:: incompressible_viscous_defaults.inc
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Examples
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--------
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shear
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^^^^^
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The same shear problem as in incompressible solver, here with viscosity
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added.
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.. prompt:: bash
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pyro_sim.py incompressible_viscous shear inputs.shear
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.. image:: shear_viscous.png
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:align: center
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Compare this with the inviscid result. Notice how the velocities have
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diffused in all directions.
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cavity
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^^^^^^
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The lid-driven cavity is a well-known benchmark problem for hydro codes
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(see e.g. :cite:t:`ghia1982`, :cite:t:`Kuhlmann2019`). In a unit square box
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with initially static fluid, motion is initiated by a "lid" at the top
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boundary, moving to the right with unit velocity. The basic command is:
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.. prompt:: bash
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pyro_sim.py incompressible_viscous cavity inputs.cavity
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It is interesting to observe what happens when varying the viscosity, or,
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equivalently the Reynolds number (in this case :math:`\rm{Re}=1/\nu` since
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the characteristic length and velocity scales are 1 by default).
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|pic1| |pic2| |pic3|
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.. |pic1| image:: cavity_Re100.png
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:width: 32%
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.. |pic2| image:: cavity_Re400.png
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:width: 32%
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.. |pic3| image:: cavity_Re1000.png
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:width: 32%
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These plots were made by allowing the code to run for longer and approach a
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steady-state with the option ``driver.max_steps=1000``, then running
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(e.g. for the Re=100 case):
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.. prompt:: bash
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python incompressible_viscous/problems/plot_cavity.py cavity_n64_Re100_0406.h5 -Re 100 -o cavity_Re100.png
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convergence
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^^^^^^^^^^^
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This is the same test as in the incompressible solver. With viscosity,
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an exponential term is added to the solution. Limiting can again be
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disabled by adding ``incompressible.limiter=0`` to the run command.
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The basic set of tests shown below are run as:
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.. prompt:: bash
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pyro_sim.py incompressible_viscous converge inputs.converge.32 vis.dovis=0
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pyro_sim.py incompressible_viscous converge inputs.converge.64 vis.dovis=0
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pyro_sim.py incompressible_viscous converge inputs.converge.128 vis.dovis=0
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The error is measured by comparing with the analytic solution using
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the routine ``incomp_viscous_converge_error.py`` in ``analysis/``. To
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generate the plot below, run
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.. prompt:: bash
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python incompressible_viscous/tests/convergence_errors.py convergence_errors.txt
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or ``convergence_errors_no_limiter.txt`` after running with that option. Then:
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.. prompt:: bash
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python incompressible_viscous/tests/convergence_plot.py
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.. image:: incomp_viscous_converge.png
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:align: center
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The solver is converging but below second-order, unlike the inviscid case. Limiting
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does not seem to make a difference here.
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Exercises
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---------
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Explorations
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^^^^^^^^^^^^
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* In the lid-driven cavity problem, when does the solution reach a steady-state?
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* :cite:`ghia1982` give benchmark velocities at different Reynolds number for the
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lid-driven cavity problem (see their Table I). Do we agree with their results?

‎docs/source/incompressible_viscous_defaults.inc‎

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* section: [driver]
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+----------------------------------+----------------+----------------------------------------------------+
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| option | value | description |
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+==================================+================+====================================================+
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| cfl | ``0.8`` | |
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+----------------------------------+----------------+----------------------------------------------------+
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* section: [incompressible]
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+----------------------------------+----------------+----------------------------------------------------+
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| option | value | description |
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+==================================+================+====================================================+
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| limiter | ``2`` | limiter (0 = none, 1 = 2nd order, 2 = 4th order) |
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+----------------------------------+----------------+----------------------------------------------------+
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| proj_type | ``2`` | what are we projecting? 1 includes -Gp term in U* |
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+----------------------------------+----------------+----------------------------------------------------+
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* section: [incompressible_viscous]
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+----------------------------------+----------------+----------------------------------------------------+
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| option | value | description |
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+==================================+================+====================================================+
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| viscosity | ``0.1`` | kinematic viscosity of the fluid (units L^2/T) |
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+----------------------------------+----------------+----------------------------------------------------+
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* section: [particles]
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+----------------------------------+----------------+----------------------------------------------------+
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| option | value | description |
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+==================================+================+====================================================+
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| do_particles | ``0`` | |
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+----------------------------------+----------------+----------------------------------------------------+
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| particle_generator | ``grid`` | |
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+----------------------------------+----------------+----------------------------------------------------+
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‎docs/source/index.rst‎

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multigrid
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diffusion_basics
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incompressible_basics
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incompressible_viscous_basics
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lowmach_basics
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swe_basics
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particles_basics

‎docs/source/pyro.incompressible_viscous.problems.rst‎

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pyro.incompressible\_viscous.problems package
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=============================================
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.. automodule:: pyro.incompressible_viscous.problems
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:members:
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:undoc-members:
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:show-inheritance:
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Submodules
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----------
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pyro.incompressible\_viscous.problems.cavity module
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---------------------------------------------------
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.. automodule:: pyro.incompressible_viscous.problems.cavity
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:members:
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:undoc-members:
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:show-inheritance:
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pyro.incompressible\_viscous.problems.converge module
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-----------------------------------------------------
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.. automodule:: pyro.incompressible_viscous.problems.converge
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:members:
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:undoc-members:
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:show-inheritance:
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pyro.incompressible\_viscous.problems.plot\_cavity module
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---------------------------------------------------------
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.. automodule:: pyro.incompressible_viscous.problems.plot_cavity
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:members:
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:undoc-members:
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:show-inheritance:
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pyro.incompressible\_viscous.problems.shear module
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--------------------------------------------------
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.. automodule:: pyro.incompressible_viscous.problems.shear
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:members:
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:undoc-members:
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:show-inheritance:

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