Merge branch 'cgw-docs' into 'main'

              'sphinx.ext.viewcode']

# Add any paths that contain templates here, relative to this directory.

templates_path = ['ytemplates']

templates_path = ['_templates']

# The suffix(es) of source filenames.

# You can specify multiple suffix as a list of string:

# -*- coding: utf-8 -*-

# Configuration for MFIX-Exa docs.

# Updated 2026-04-30, Charles G Waldman

#

# amrex documentation build configuration file, created by

# sphinx-quickstart on Thu Oct 19 14:30:08 2017.

#

# This file is execfile()d with the current directory set to its

# containing dir.

#

# Note that not all possible configuration values are present in this

# autogenerated file.

#

# All configuration values have a default; values that are commented out

# serve to show the default.

# If extensions (or modules to document with autodoc) are in another directory,

# add these directories to sys.path here. If the directory is relative to the

# documentation root, use os.path.abspath to make it absolute, like shown here.

#

# import os

# import sys

# sys.path.insert(0, os.path.abspath('.'))

import sphinx_rtd_theme

# -- General configuration ------------------------------------------------

# If your documentation needs a minimal Sphinx version, state it here.

              'sphinxcontrib.bibtex' ]

# Add any paths that contain templates here, relative to this directory.

templates_path = ['ytemplates']

templates_path = ['_templates']

# No highlighting unless specified

highlight_language = 'none'

# The suffix(es) of source filenames.

# You can specify multiple suffix as a list of string:

# General information about the project.

project = u'MFIX-Exa'

copyright = u'2017-2018, MFIX-Exa Team'

copyright = u'2017-2026, MFIX-Exa Team'

author = u'MFIX-Exa Team'

# The version info for the project you're documenting, acts as replacement for

# The theme to use for HTML and HTML Help pages.  See the documentation for

# a list of builtin themes.

#

html_theme = 'sphinx_rtd_theme'

# Theme options are theme-specific and customize the look and feel of a theme

# further.  For a list of options available for each theme, see the

# documentation.

#

html_theme_options = {

    'logo_only': False,

    'prev_next_buttons_location': 'bottom',

    'style_external_links': False,

    'vcs_pageview_mode': '',

    # Toc options

    'collapse_navigation': True,

    'sticky_navigation': True,

    'navigation_depth': 4,

    'includehidden': True,

    'titles_only': False

}

#html_theme = 'sphinx_rtd_theme'

html_theme = 'furo'

html_show_sourcelink = False

# Add any paths that contain custom static files (such as style sheets) here,

# relative to this directory. They are copied after the builtin static files,

#

# This is required for the alabaster theme

# refs: http://alabaster.readthedocs.io/en/latest/installation.html#sidebars

html_sidebars = {

    '**': [

        'about.html',

        'navigation.html',

        'relations.html',  # needs 'show_related': True theme option to display

        'searchbox.html',

        'donate.html',

    ]

}

# -- Options for HTMLHelp output ------------------------------------------

# Output file base name for HTML help builder.

htmlhelp_basename = 'amrexdoc'

# html_sidebars = {

#     '**': [

#         'about.html',

#         'navigation.html',

#         'relations.html',  # needs 'show_related': True theme option to display

#         'searchbox.html',

#         'donate.html',

#     ]

# }

# -- Options for LaTeX output ---------------------------------------------

}

# Use longtable for better page breaks and wrapping

latex_table_style = ['longtable', 'colorrows']

# Force SVG for mathjax equations, avoids line height issues

# with CHTML

mathjax_path = 'https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js'

# Keep users from selecting CHTML via menu

mathjax3_config = {

    'options': {

        'enableMenu': False,

        'menuOptions': {

            'settings': {

                'renderer': 'svg',

            }

        }

    }

}

using the names provided in the inputs file. Similarly, the reaction rate

is stored using the name given in the inputs file.

.. code-block:: bash

.. code-block:: text

   :caption: Snippet of inputs defining fluid species and adiabatic flame reaction

   # Fluid model settings

Creating the MAC velocities

~~~~~~~~~~~~~~~~~~~~~~~~~~~

Creating the MAC (Marker and Cell) velocities

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To create the normal velocities on faces, we first extrapolate from the cell centers on each side using the

slopes as computed earlier, and upwind the face value to define  :math:`U^{pred}`

slopes as computed earlier, and upwind the face value to define  :math:`U^{pred}`.

.  To compute the x-velocity on the x-faces of regular (ie not cut) cells, we call

To compute the x-velocity on the x-faces of regular (ie not cut) cells, we call

   .. code:: shell

   .. code-block:: cpp

            AMREX_CUDA_HOST_DEVICE_FOR_3D(ubx, i, j, k,

             {

For cut cells we test on whether the area fraction is non-zero:

   .. code:: shell

   .. code-block:: cpp

             AMREX_CUDA_HOST_DEVICE_FOR_3D(ubx, i, j, k,

             {

Computing slopes

~~~~~~~~~~~~~~~~~~~~~~~~~~~

================

Slopes are computed one direction at a time for each scalar and each

velocity component.

limiter (van Leer, 1977). The scheme is described below for the u-velocity.

The limiter computes the slope at cell "i" by combining the left, central

and right u-variation "du":

.. code:: shell

and right u-variation "du"::

     du_l = u(i) - u(i-1)               = left variation

     du_c = 0.5 * ( u(i+1) - u(i-1) )   = central (umlimited) variation

     du_c = 0.5 * ( u(i+1) - u(i-1) )   = central (unlimited) variation

     du_r = u(i+1) - u(i)               = right variation

Finally, the u-variation at cell "i" is given by :

.. code:: shell

Finally, the u-variation at cell "i" is given by::

     du(i) = sign(du_c) * min(2|du_l|, |du_c|, 2|du_r|)) if du_l*du_r > 0

     du(i) = 0                                           otherwise

The above procedure is applied direction by direction.

BOUNDARY CONDITIONS

When periodic or Neumann's BCs are imposed, the scheme can be applied

Boundary conditions

-------------------

When periodic or Neumann BCs are imposed, the scheme can be applied

without any change since the ghost cells at the boundary are filled

by either periodicity or by extrapolation.

For Dirichlet's BCs in the transversal direction, the scheme can again

For Dirichlet BCs in the transversal direction, the scheme can again

be applied as is since the velocity is known at the first ghost cell

out of the domain.

However, for Dirichlet's BCs in the longitudinal direction, the velocity

However, for Dirichlet BCs in the longitudinal direction, the velocity

is not known outside the domain since the BC is applied directly at the first

valid node which lies on the boundary itself. Therefore, the scheme must be

arranged as follows to use ONLY values from inside the domain.

For a left boundary (i=0), the u-variations are:

.. code:: shell

For a left boundary (i=0), the u-variations are::

     du_l = 0                             Dont use values on the left

     du_l = 0                             Don't use values on the left

     du_c = -1.5*u(0) + 2*u(1) -0.5*u(2)  2nd order right-biased

     du_r = u(1) - u(0)                   Right variation