update docs

              '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:

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

*  For the dependencies, it is assumed that you have set the

   following environment variables:

   .. code:: bash

   .. code-block:: bash

      export HYPRE_INSTALL_DIR=$HOME/<path/to/my/hypre-install-dir>

      export CSG_INSTALL_DIR=$HOME/<path/to/my/csg-dep-install-dir>

There are (basically) no modules loaded by default on Bridges-2.

.. code:: bash

.. code-block:: bash

    module load gcc/10.2.0                 # PrgEnv

    module load openmpi/4.0.5-gcc10.2.0    # MPI

   .. tab:: CPU

      .. code:: bash

      .. code-block:: bash

         cp -r exec exec.cpu

         make -C exec.cpu -j8 \

   .. tab:: GPU

      .. code:: bash

      .. code-block:: bash

         cp -r exec exec.gpu

         make -C exec.gpu -j8 \

   .. tab:: CPU-full

      .. code:: bash

      .. code-block:: bash

         export HYPRE_DIR=$HYPRE_INSTALL_DIR

         export HYPRE_HOME=$HYPRE_DIR

   .. tab:: GPU-full

      .. code:: bash

      .. code-block:: bash

         export HYPRE_DIR=$HYPRE_INSTALL_DIR

         export HYPRE_HOME=$HYPRE_DIR

      .. tab:: CPU

         .. code:: bash

         .. code-block:: bash

            git clone https://github.com/hypre-space/hypre.git

            pushd hypre/src/

      .. tab:: GPU

         .. code:: bash

         .. code-block:: bash

            git clone https://github.com/hypre-space/hypre.git

            pushd hypre/src/

   ``export CMAKE_INSTALL_DIR=$HOME/<path/to/my/cmake-install-dir>``

   to a path that you have read/write access to.

   .. code:: bash

   .. code-block:: bash

      wget https://cmake.org/files/v3.23/cmake-3.23.2.tar.gz

      tar -zxvf cmake-3.23.2.tar.gz

   After installing cmake, you will need to prepend it to your path

   .. code:: bash

   .. code-block:: bash

      export PATH=$CMAKE_INSTALL_DIR/bin:$PATH

#. Catch2

   .. code:: bash

   .. code-block:: bash

      git clone --depth 1 --branch v3.11.0 https://github.com/catchorg/Catch2

      pushd Catch2/

#. GMP

   .. code:: bash

   .. code-block:: bash

      wget --no-check-certificate https://ftp.gnu.org/gnu/gmp/gmp-6.2.1.tar.xz

      tar -xf gmp-6.2.1.tar.xz

#. MPFR

   .. code:: bash

   .. code-block:: bash

      wget --no-check-certificate https://ftp.gnu.org/gnu/mpfr/mpfr-4.1.0.tar.xz

      tar -xf mpfr-4.1.0.tar.xz

#. CGAL

   .. code:: bash

   .. code-block:: bash

      git clone --depth 1 --branch v6.1.1 https://github.com/CGAL/cgal

      pushd cgal/

#. PEGTL

   .. code:: bash

   .. code-block:: bash

      git clone --branch 3.2.8 https://github.com/taocpp/PEGTL

      pushd PEGTL/

   Make sure you have boost loaded before building. (This is intended to be

   executed from inside the mfix repo.)

   .. code:: bash

   .. code-block:: bash

      make -C subprojects/csg-eb install DESTDIR=$CSG_LIB_DIR \

           PEGTL_HOME=$CSG_INSTALL_DIR \

#. Conduit

   .. code:: bash

   .. code-block:: bash

      git clone --recursive https://github.com/LLNL/conduit.git

      pushd conduit/

#. Vtk-m

   .. code:: bash

   .. code-block:: bash

      git clone --branch master https://gitlab.kitware.com/vtk/vtk-m.git

      pushd vtk-m/

#. Ascent

   .. code:: bash

   .. code-block:: bash

      git clone --recursive https://github.com/Alpine-DAV/ascent.git

      pushd ascent

interactive commands above to convert this into a shared job script.

CPU-only runs have not been tested on this machine.

.. code:: bash

.. code-block:: bash

   #!/bin/bash

   #!/bin/bash

* For the dependencies, it is assumed that you have set the

  following environment variables:

  .. code:: bash

  .. code-block:: bash

     export HYPRE_INSTALL_DIR=$HOME/<path/to/my/hypre-install-dir>

     export CSG_INSTALL_DIR=$HOME/<path/to/my/csg-dep-install-dir>

  build the PIC-to-DEM restarter app by executing the following command

  in the ``build`` directory

  .. code:: bash

  .. code-block:: bash

      cmake --build . --target pic2dem

   .. tab:: PrgEnv-cray

      .. code:: bash

      .. code-block:: bash

         module purge

         module reset

      Modules

      .. code:: bash

      .. code-block:: bash

         module purge

         module reset

      CPU compilers

      .. code:: bash

      .. code-block:: bash

         export CC=$(which cc)

         export CXX=$(which CC)

      GPU compilers

      .. code:: bash

      .. code-block:: bash

         export CC=$(which hipcc)

         export CXX=$(which hipcc)

   .. tab:: CPU

      .. code:: bash

      .. code-block:: bash

         cmake -DMFIX_MPI=yes \

               -DMFIX_OMP=no \

   .. tab:: GPU

      .. code:: bash

      .. code-block:: bash

         export AMREX_AMD_ARCH=gfx90a

   .. tab:: CPU-full

      .. code:: bash

      .. code-block:: bash

         export HYPRE_DIR=$HYPRE_INSTALL_DIR

         export HYPRE_ROOT=$HYPRE_DIR

   .. tab:: GPU-full

      .. code:: bash

      .. code-block:: bash

         export HYPRE_DIR=$HYPRE_INSTALL_DIR

         export HYPRE_ROOT=$HYPRE_DIR

      .. tab:: CPU

         .. code:: bash

         .. code-block:: bash

            git clone https://github.com/hypre-space/hypre.git

            pushd hypre/src/

      .. tab:: GPU

         .. code:: bash

         .. code-block:: bash

            git clone https://github.com/hypre-space/hypre.git

            pushd hypre/src/

#. Catch2

   .. code:: bash

   .. code-block:: bash

      git clone --depth 1 --branch v3.11.0 https://github.com/catchorg/Catch2

      pushd Catch2/

#. GMP

   .. code:: bash

   .. code-block:: bash

      wget --no-check-certificate https://ftp.gnu.org/gnu/gmp/gmp-6.2.1.tar.xz

      tar -xf gmp-6.2.1.tar.xz

#. MPFR

   .. code:: bash

   .. code-block:: bash

      wget https://www.mpfr.org/mpfr-current/mpfr-4.2.0.tar.gz

      tar -zxvf mpfr-4.2.0.tar.gz

#. CGAL

   .. code:: bash

   .. code-block:: bash

      git clone --depth 1 --branch v6.1.1 https://github.com/CGAL/cgal

      pushd cgal/

#. PEGTL

   .. code:: bash

   .. code-block:: bash

      git clone --branch 3.2.8 https://github.com/taocpp/PEGTL

      pushd PEGTL/

   Make sure that "experimental" precedes filesystem on or near lines 47 and 51 in

   ``CSG_INSTALL_DIR/include/tao/pegtl/internal/filesystem.hpp``

   .. code:: bash

   .. code-block:: bash

      ...

      #include <experimental/filesystem>

#. Boost

   .. code:: bash

   .. code-block:: bash

      wget https://boostorg.jfrog.io/artifactory/main/release/1.81.0/source/boost_1_81_0.tar.gz

      tar -zxvf boost_1_81_0.tar.gz

#. Conduit

   .. code:: bash

   .. code-block:: bash

      git clone --recursive https://github.com/LLNL/conduit.git

      pushd conduit/

#. Vtk-m

   .. code:: bash

   .. code-block:: bash

      git clone --branch master https://gitlab.kitware.com/vtk/vtk-m.git

      pushd vtk-m/

#. Ascent

   .. code:: bash

   .. code-block:: bash

      git clone --recursive https://github.com/Alpine-DAV/ascent.git

      pushd ascent

   .. tab:: PrgEnv-cray

      .. code:: bash

      .. code-block:: bash

         #!/bin/bash -l

   .. tab:: PrgEnv-gnu

      .. code:: bash

      .. code-block:: bash

         #!/bin/bash -l