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better formatting for parameters
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‎docs/source/_defaults.inc‎

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* section: [driver]
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**driver**
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+----------------------------------+----------------+----------------------------------------------------+
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| option | value | description |
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+==================================+================+====================================================+
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| tmax | ``1.0`` | maximum simulation time to evolve |
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+----------------------------------+----------------+----------------------------------------------------+
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| max_steps | ``10000`` | maximum number of steps to take |
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+----------------------------------+----------------+----------------------------------------------------+
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| fix_dt | ``-1.0`` | |
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+----------------------------------+----------------+----------------------------------------------------+
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| init_tstep_factor | ``0.01`` | first timestep = init_tstep_factor * CFL timestep |
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+----------------------------------+----------------+----------------------------------------------------+
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| max_dt_change | ``2.0`` | max amount the timestep can change between steps |
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+----------------------------------+----------------+----------------------------------------------------+
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| verbose | ``1.0`` | verbosity |
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+----------------------------------+----------------+----------------------------------------------------+
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+----------------------------------+------------+----------------------------------------------------+
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| option | value | description |
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+==================================+============+====================================================+
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| tmax | 1.0 | maximum simulation time to evolve |
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+----------------------------------+------------+----------------------------------------------------+
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| max_steps | 10000 | maximum number of steps to take |
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+----------------------------------+------------+----------------------------------------------------+
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| fix_dt | -1.0 | |
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+----------------------------------+------------+----------------------------------------------------+
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| init_tstep_factor | 0.01 | first timestep = init_tstep_factor * CFL timestep |
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+----------------------------------+------------+----------------------------------------------------+
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| max_dt_change | 2.0 | max amount the timestep can change between steps |
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+----------------------------------+------------+----------------------------------------------------+
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| verbose | 1.0 | verbosity |
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+----------------------------------+------------+----------------------------------------------------+
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* section: [io]
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**io**
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+----------------------------------+----------------+----------------------------------------------------+
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| option | value | description |
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+==================================+================+====================================================+
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| basename | ``pyro_`` | basename for output files |
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+----------------------------------+----------------+----------------------------------------------------+
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| dt_out | ``0.1`` | simulation time between writing output files |
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+----------------------------------+----------------+----------------------------------------------------+
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| n_out | ``10000`` | number of timesteps between writing output files |
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+----------------------------------+----------------+----------------------------------------------------+
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| do_io | ``1`` | do we output at all? |
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+----------------------------------+----------------+----------------------------------------------------+
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+----------------------------------+------------+----------------------------------------------------+
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| option | value | description |
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+==================================+============+====================================================+
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| basename | pyro_ | basename for output files |
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+----------------------------------+------------+----------------------------------------------------+
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| dt_out | 0.1 | simulation time between writing output files |
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+----------------------------------+------------+----------------------------------------------------+
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| n_out | 10000 | number of timesteps between writing output files |
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+----------------------------------+------------+----------------------------------------------------+
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| do_io | 1 | do we output at all? |
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+----------------------------------+------------+----------------------------------------------------+
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* section: [mesh]
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**mesh**
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+----------------------------------+----------------+----------------------------------------------------+
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| option | value | description |
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+==================================+================+====================================================+
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| xmin | ``0.0`` | domain minumum x-coordinate |
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+----------------------------------+----------------+----------------------------------------------------+
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| xmax | ``1.0`` | domain maximum x-coordinate |
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+----------------------------------+----------------+----------------------------------------------------+
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| ymin | ``0.0`` | domain minimum y-coordinate |
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+----------------------------------+----------------+----------------------------------------------------+
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| ymax | ``1.0`` | domain maximum y-coordinate |
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+----------------------------------+----------------+----------------------------------------------------+
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| xlboundary | ``reflect`` | minimum x BC ('reflect', 'outflow', or 'periodic') |
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+----------------------------------+----------------+----------------------------------------------------+
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| xrboundary | ``reflect`` | maximum x BC ('reflect', 'outflow', or 'periodic') |
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+----------------------------------+----------------+----------------------------------------------------+
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| ylboundary | ``reflect`` | minimum y BC ('reflect', 'outflow', or 'periodic') |
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+----------------------------------+----------------+----------------------------------------------------+
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| yrboundary | ``reflect`` | maximum y BC ('reflect', 'outflow', or 'periodic') |
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+----------------------------------+----------------+----------------------------------------------------+
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| nx | ``25`` | number of zones in the x-direction |
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+----------------------------------+----------------+----------------------------------------------------+
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| ny | ``25`` | number of zones in the y-direction |
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+----------------------------------+----------------+----------------------------------------------------+
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+----------------------------------+------------+----------------------------------------------------+
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| option | value | description |
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+==================================+============+====================================================+
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| xmin | 0.0 | domain minumum x-coordinate |
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+----------------------------------+------------+----------------------------------------------------+
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| xmax | 1.0 | domain maximum x-coordinate |
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+----------------------------------+------------+----------------------------------------------------+
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| ymin | 0.0 | domain minimum y-coordinate |
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+----------------------------------+------------+----------------------------------------------------+
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| ymax | 1.0 | domain maximum y-coordinate |
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+----------------------------------+------------+----------------------------------------------------+
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| xlboundary | reflect | minimum x BC ('reflect', 'outflow', or 'periodic') |
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+----------------------------------+------------+----------------------------------------------------+
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| xrboundary | reflect | maximum x BC ('reflect', 'outflow', or 'periodic') |
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+----------------------------------+------------+----------------------------------------------------+
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| ylboundary | reflect | minimum y BC ('reflect', 'outflow', or 'periodic') |
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+----------------------------------+------------+----------------------------------------------------+
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| yrboundary | reflect | maximum y BC ('reflect', 'outflow', or 'periodic') |
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+----------------------------------+------------+----------------------------------------------------+
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| nx | 25 | number of zones in the x-direction |
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+----------------------------------+------------+----------------------------------------------------+
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| ny | 25 | number of zones in the y-direction |
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+----------------------------------+------------+----------------------------------------------------+
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* section: [particles]
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**particles**
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+----------------------------------+----------------+----------------------------------------------------+
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| option | value | description |
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+==================================+================+====================================================+
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| do_particles | ``0`` | include particles? (1=yes, 0=no) |
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+----------------------------------+----------------+----------------------------------------------------+
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| n_particles | ``100`` | number of particles |
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+----------------------------------+----------------+----------------------------------------------------+
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| particle_generator | ``random`` | how do we generate particles? (random, grid) |
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+----------------------------------+----------------+----------------------------------------------------+
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+----------------------------------+------------+----------------------------------------------------+
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| option | value | description |
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+==================================+============+====================================================+
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| do_particles | 0 | include particles? (1=yes, 0=no) |
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+----------------------------------+------------+----------------------------------------------------+
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| n_particles | 100 | number of particles |
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+----------------------------------+------------+----------------------------------------------------+
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| particle_generator | random | how do we generate particles? (random, grid) |
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+----------------------------------+------------+----------------------------------------------------+
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* section: [vis]
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**vis**
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+----------------------------------+----------------+----------------------------------------------------+
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| option | value | description |
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+==================================+================+====================================================+
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| dovis | ``1`` | runtime visualization? (1=yes, 0=no) |
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+----------------------------------+----------------+----------------------------------------------------+
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| store_images | ``0`` | store vis images to files (1=yes, 0=no) |
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+----------------------------------+----------------+----------------------------------------------------+
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+----------------------------------+------------+----------------------------------------------------+
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| option | value | description |
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+==================================+============+====================================================+
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| dovis | 1 | runtime visualization? (1=yes, 0=no) |
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+----------------------------------+------------+----------------------------------------------------+
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| store_images | 0 | store vis images to files (1=yes, 0=no) |
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+----------------------------------+------------+----------------------------------------------------+

‎docs/source/advection_basics.rst‎

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compressible hydrodynamics. Chapter 4 of the notes summarizes the
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numerical methods for advection that we implement in pyro.
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pyro has several solvers for linear advection:
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pyro has several solvers for linear advection, which solve the equation
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with different spatial and temporal intergration schemes.
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* :py:mod:`advection` implements the directionally unsplit corner transport upwind
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algorithm with piecewise linear reconstruction
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``advection`` solver
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--------------------
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* :py:mod:`advection_fv4` uses a fourth-order accurate finite-volume
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method with RK4 time integration
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:py:mod:`advection` implements the directionally unsplit corner
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transport upwind algorithm :cite:`colella:1990` with piecewise linear reconstruction.
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This is an overall second-order accurate method, with timesteps restricted
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by
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* :py:mod:`advection_nonuniform` models advection with a non-uniform velocity field.
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This is used to implement
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`Zalesak (1979) <https://doi.org/10.1016/0021-9991(79)90051-2>`_'s slotted disk problem.
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.. math::
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\Delta t < \min \left \{ \frac{\Delta x}{|u|}, \frac{\Delta y}{|v|} \right \}
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The parameters for this solver are:
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.. include:: advection_defaults.inc
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``advection_fv4`` solver
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------------------------
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:py:mod:`advection_fv4` uses a fourth-order accurate finite-volume
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method with RK4 time integration, following the ideas in
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:cite:`mccorquodalecolella`. It can be thought of as a
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method-of-lines integration, and as such has a slightly more restrictive
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timestep:
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.. math::
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\Delta t \lesssim \left [ \frac{|u|}{\Delta x} + \frac{|v|}{\Delta y} \right ]^{-1}
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The main complexity comes from needing to average the flux over the
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faces of the zones to achieve 4th order accuracy spatially.
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The parameters for this solver are:
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.. include:: advection_fv4_defaults.inc
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* :py:mod:`advection_rk` uses a method of lines time-integration
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approach with piecewise linear spatial reconstruction for linear
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advection
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``advection_nonuniform`` solver
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-------------------------------
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* :py:mod:`advection_weno` uses a WENO reconstruction and method of
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lines time-integration
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:py:mod:`advection_nonuniform` models advection with a non-uniform
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velocity field. This is used to implement the slotted disk problem
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from :cite:`ZALESAK1979335`. The basic method is similar to the
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algorithm used by the main ``advection`` solver.
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The paramters for this solver are:
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.. include:: advection_nonuniform_defaults.inc
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``advection_rk`` solver
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-----------------------
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:py:mod:`advection_rk` uses a method of lines time-integration
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approach with piecewise linear spatial reconstruction for linear
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advection. This is overall second-order accurate, so it represents a
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simpler algorithm than the ``advection_fv4`` method (in particular, we
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can treat cell-centers and cell-averages as the same, to second
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order).
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The parameter for this solver are:
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.. include:: advection_rk_defaults.inc
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``advection_weno`` solver
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-------------------------
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:py:mod:`advection_weno` uses a WENO reconstruction and method of
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lines time-integration
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The main parameters that affect this solver are:
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+-------------------------------------------------------------------------------------------------------------------------------+
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| ``[driver]`` |
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+=====================+=========================================================================================================+
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|``cfl`` | the advective CFL number (what fraction of a zone can we cross in a single timestep) |
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+---------------------+---------------------------------------------------------------------------------------------------------+
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+-------------------------------------------------------------------------------------------------------------------------------+
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| ``[advection]`` |
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+=====================+=========================================================================================================+
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|``u`` | the advective velocity in the x direction |
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+---------------------+---------------------------------------------------------------------------------------------------------+
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|``v`` | the advective velocity in the y direction |
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+---------------------+---------------------------------------------------------------------------------------------------------+
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|``limiter`` | what type of limiting to use in reconstructing the slopes. 0 means use an unlimited second-order |
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| | centered difference. 1 is the MC limiter, and 2 is the 4th-order MC limiter |
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+---------------------+---------------------------------------------------------------------------------------------------------+
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|``temporal_method`` | the MOL integration method to use (RK2, TVD2, TVD3, RK4) (advection_rk only) |
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+---------------------+---------------------------------------------------------------------------------------------------------+
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.. include:: advection_weno_defaults.inc
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General ideas
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-------------
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The main use for the advection solver is to understand how Godunov
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techniques work for hyperbolic problems. These same ideas will be used

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