Merge branch 'master' of https://github.com/AMReX-Codes/MFIX-Exa

| AMREX\_CXX\_FLA | User-defined C++ flags for   | valid C++        | None        |

| GS              | AMReX build                  | compiler flags   |             |

+-----------------+------------------------------+------------------+-------------+

| ENABLE\_MPI     | Enable build with MPI        | 0/1              | 1           |

|                 |                              |                  |             |

+-----------------+------------------------------+------------------+-------------+

| ENABLE\_OMP     | Enable build with OpenMP     | 0/1              | 0           |

|                 |                              |                  |             |

+-----------------+------------------------------+------------------+-------------+

| ENABLE\_FPE     | Build with Floating-Point    | 0/1              | 0           |

|                 | Exceptions checks            |                  |             |

+-----------------+------------------------------+------------------+-------------+

.. _Chap:EB:

Embedded Boundaries

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

MFiX-Exa uses AMReX's Embedded Boundaries to represent container walls. This

allows MFiX-Exa to simulate a wide range of shapes and boundary conditions using

constructive solid geometry. MFiX-Exa also has the capability of locally

refining the computational meshes near walls.

.. toctree::

   :maxdepth: 1

   :caption: Contents:

   EBWalls

.. role:: cpp(code)

   :language: c++

.. role:: fortran(code)

   :language: fortran

.. _sec:EB-basics:

Constructing Embedded Boundaries in MFiX-Exa

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

MFiX uses AMReX's constructive solid geometry framework defined in the namespace

:cpp:`amrex::EB2`. See the `AMReX EB documentation`_ for more details. These are

defined in ``src/eb/mfix_eb.cpp``. A the function :cpp:`mfix::make_eb_geometry`

(also defined in ``src/eb/mfix_eb.cpp``) selects :cpp:one of the following

geometries depending on the value of the :cpp:``mfix.geometry`` setting in the

``inputs`` file.

+------------------------------+----------------------+-------------------------+

|   Description                |  ``mfix.geometry``   |   Implementation Satus  |

+==============================+======================+=========================+

| Planar walls from mfix.dat   | Don't specify        | Fully implemented       |

| (on by default)              |                      |                         |

+------------------------------+----------------------+-------------------------+

| Box (up to six walls)        | ``box``              | Fully implemented       |

+------------------------------+----------------------+-------------------------+

| Cylinder                     | ``cylinder``         | Fully implemented       |

+------------------------------+----------------------+-------------------------+

| Hopper                       | ``hopper``           | Fully implemented       |

+------------------------------+----------------------+-------------------------+

| Cyclone                      | ``cyclone``          | Fully implemented       |

+------------------------------+----------------------+-------------------------+

| General                      | ``general``          | Partially implemented   |

|                              | cf. note 1 below     |                         |

+------------------------------+----------------------+-------------------------+

| Hourglass                    | ``hourglass``        | Deprecated              |

|                              | cf. note 1           | cf. note 2 below        |

+------------------------------+----------------------+-------------------------+

| CLR (chemical looping        | ``clr``              | Deprecated              |

| reactor)                     | cf. note 1           | cf. note 2              |

+------------------------------+----------------------+-------------------------+

| CLR Riser                    | ``clr_riser``        | Deprecated              |

|                              | cf. note 1           | cf. note 2              |

+------------------------------+----------------------+-------------------------+

1. Older (legacy) alternative settings are:

   +-----------------------------+-------------------------------+

   | Value of  ``mfix.geometry`` |  Alternative                  |

   +=============================+===============================+

   | ``general``                 | ``mfix.use_poly2 = true``     |

   |                             | or ``mfix.use_walls = true``  |

   +-----------------------------+-------------------------------+

   | ``hourglass``               | ``mfix.hourglass = true``     |

   +-----------------------------+-------------------------------+

   | ``clr``                     | ``mfix.clr = true``           |

   +-----------------------------+-------------------------------+

   | ``clr_riser``               | ``mfix.clr_riser = true``     |

   +-----------------------------+-------------------------------+

2. These geometries where not ported from AMReX's old :cpp:``EB`` system to the

   new :cpp:``EB2``.

Also note that planar boundary conditions can be specified in the ``mfix.dat``

file. Even if the user does not specify an ``mfix.geometry`` in the ``inputs``,

any no-slip or free-slip boundary conditions are expressed as EB walls.

There are also two parameters (specified in the ``inputs`` file) that influence

the level-set creation:

+-------------------------------+------------------------------------------------+

|  Parameter                    |  Description                                   |

+===============================+================================================+

| ``amr.max_level``             | If greater than 1, MFiX operates in multi-level|

|                               | mode. The level-set grids follow all other     |

|                               | grids. If equal to 1, the level-set has two    |

|                               | levels (one additional level with higher       |

|                               | refinement).                                   |

+-------------------------------+------------------------------------------------+

| ``mfix.levelset__refinement`` | If ``amr.max_level > 1`` this parameter is     |

|                               | ignored. Otherwise it sets the maximum         |

|                               | refinement of the level-set                    |

+-------------------------------+------------------------------------------------+

How MFiX-Exa Constructs the EB Geometry

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

Once a geometry is selected by :cpp:`mfix::make_eb_geometry`, the procedure is

the same for (almost) all geometries. Also see the `AMReX geometry

documentation`_ for information on how to construct new geometries:

1. Construct an implicit function representing the geometry (using the language

   of constructive solid geometry). For example

.. highlight:: c++

::

   EB2::CylinderIF my_cyl(radius, height, direction, center, inside);

   auto gshop_cyl = EB2::makeShop(my_cyl);

2. (Optional) Construct the implicit function representing the EB seen by the

   particles. This might deviate from the "standard" EB depending on the

   specific application. In all standard cases used by mfix, this step is

   omitted.

3. Call :cpp:`mfix::build_eb_levels(gshop)` this function builds the EB levels

   and fills the implicit function :cpp:`MultiFab` (the later being used to

   construct the level-set function). Note that this also makes the particle EB

   levels point to the fluid eb levels.

4. (Optional, do this if you did 2.) Call

   :cpp:`mfix::build_particle_eb_levels(gshop_part)` **last**. This will update

   the particle EB levels.

MFiX's EB Data Structures

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

The :cpp:`mfix` class stores the following EB data:

.. highlight:: c++

::

   //! EB levels representing fluid boundary conditions

   Vector<const EB2::Level *> eb_levels;

   //! EB levels representing particle boundary conditions (same as

   //! `mfix::eb_levels` but might include additional walls).

   Vector<const EB2::Level *> particle_eb_levels;

   //! EB factory that lives on the fluid grids

   Vector< std::unique_ptr<amrex::EBFArrayBoxFactory> > ebfactory;

   //! EB factory that lives on the particle grids

   Vector< std::unique_ptr<amrex::EBFArrayBoxFactory> > particle_ebfactory;

As discussed in the previous sub-section, the difference between

:cpp:`mfix::eb_levels` and :cpp:`mfix::particle_eb_levels` enables the user to

specify a modfied EB geometry for particles only. Whereas the fluid sees the EB

geometry in :cpp:`mfix::eb_levels`. If no addition particle EB geometry is

specified (point 4 in the previous section), then

:cpp:`mfix::particle_eb_levels` points to :cpp:`mfix::eb_levels`.

In the same spirit, the :cpp:`mfix::ebfactory` is constructed over the fluid

grid and using the fluid EB levels, whereas :cpp:`mfix::particle_ebfactory` is

constructed over the particle grid using the particle EB levels.

A note about constructing EB Levels

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

MFiX-Exa builds EB levels in :cpp:`mfix::build_eb_levels` (via

:cpp:`LSCore<F>::BuildEBLevel`)

.. highlight:: c++

::

   EB2::Build(gshop, geom[lev], required_crse_lev, max_crse_level);

   const EB2::IndexSpace & ebis = EB2::IndexSpace::top();

When building an EB level, the maximum coarsening level (:cpp:`int

max_crse_level`) and the required coarsening level (:cpp:`int

required_crse_lev`) need to be specified. The reason for this is that we need to

specify to which level of coarseness the EB is still defined. It might not be

immediately obvious, but the Poisson solver (used in the fluid solve) also

depends indirectly on these parameters. Thus changing these during EB level

creation might restrict how many levels the MLMG solver can use, and therefore

give slightly different answers in the fluid solve.

Local Mesh Refinement at Walls

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

MFiX-Exa has the capability of locally refining the computational grid near EBs.

This is done by tagging (in :cpp:`mfix::ErrorEst`) any cells with volume

fraction between 0 and 1. To enable local mesh refinement, set ``amr.max_level``

to a value greater than 1. Note that the parameter ``mfix.levelset__refinement``

is ignored on all cases except when ``amr.max_level = 1``.

MFiX-Exa Initialization Process

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

Since MFiX requires the volume fraction when building grids (because this is

needed by :cpp:`mfix::ErrorEst`), the EB geometries need to be built before

calling :cpp:`mfix::Init`. The recommended procedure therefore is

.. highlight:: c++

::

   // Default constructor (geom[lev] is defined here)

   mfix my_mfix;

   // Initialize internals from ParamParse database

   my_mfix.InitParams(solve_fluid, solve_dem, call_udf);

   // Initialize memory for data-array internals

   my_mfix.ResizeArrays();

   // Construct EB (must be done _before_ mfix::Init)

   my_mfix.make_eb_geometry();

   // Initialize derived internals. Grids are create here.

   my_mfix.Init(dt, time);

   // Create EB factories on new grids

   my_mfix.make_eb_factories();

   if (solve_dem)

   {

       // Fill level-sets on each level (must be done _after_ mfix::Init)

       my_mfix.fill_eb_levelsets();

   }

   // Finish constructing levels

   my_mfix.InitLevelData(dt,time);

   // Regrid (ensure all MultiFabs are on their correct grids)

   my_mfix.Regrid();

Also note that mfix defines boundary conditions in Fortran also (via the

mfix.dat). Since these are potentially needed to build EB walls,

:cpp:`mfix::make_eb_geometry` also calls :cpp:`mfix_set_bc_type`.

The grids for each level are build in the :cpp:`mfix::Init` by invoking the

initialization functions inherited from :cpp:`amrex::AmrCore`.

.. highlight:: c++

::

   // This tells the AmrMesh class not to iterate when creating the initial

   // grid hierarchy

   SetIterateToFalse();

   // This tells the Cluster routine to use the new chopping routine which

   // rejects cuts if they don't improve the efficiency

   SetUseNewChop();

   // This Builds the new Grids

   InitFromScratch(0.);

The Level-Set Function

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

MFiX-Exa uses a level-set function to resolve particle-wall collisions. See the

`AMReX Level-Set documentation`_ for more details. The level-set function is

stored on the nodal :cpp:`Vector<std::unique_ptr<MultiFab>> mfix::level_sets`.

The level-set data is always stored on the particle grids. Depending on the

input ``amr.max_level`` The level-set can be in one of two modes:

1. MFiX-Exa is running in single-level mode (:cpp:`nlev == 1`). Then

   :cpp:`mfix::level_sets[0]` will be at the same resolution as the fluid

   (except that it is stored on the particle grid). Even though :cpp:`nlev == 1`,

   there is a second level, :cpp:`level_sets[1]`. This level is the same as

   :cpp:`level_sets[0]` but refined by :cpp:`mfix::levelset__refinement`. This

   way the level-set always has the appropriate resolution to resolve structures

   in the EB, even if the fluid is defined on a fairly coarse grid.

2. MFiX-Exa is running in multi-level mode (:cpp:`nlev > 1`). The the parameter

   :cpp:`mfix::levelset__refinement` is ignored. :cpp:`mfix::level_sets` then

   follows the rest of MFiX, i.e. it is defined on the particle grids on all

   levels.

The level-set is used in two places:

1. The function :cpp:`MFIXParticleContainer::EvolveParticles` interpolates the

   level-set onto each particle's position in order to resolve collisions with

   the EBs. If :cpp:`nlev == 1`, :cpp:`level_sets[1]` is used to evolve the

   particle positions. Otherwise :cpp:`level_sets[lev]` is used for each level.

2. The fluid-particle coupling can sometimes rely on neighbor stencils where one

   or more cell is covered by an EB. In order to avoid values that do not

   conform with the boundary conditions, the fluid velocity is reconstructed in

   those cells. The algorithm relies on the level-set, and uses

   :cpp:`level_sets[lev]` on each level.

Special Cases Involving Level-Sets

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

The level-set function is filled by the `mfix::fill_eb_levelsets()` function.

There are two special cases involving level-sets:

1. Mass-Inflow boundary conditions are not given EB walls. However, we don't

   want particles to fall out of a MI either, so at the very end of the

   `mfix::fill_eb_levelsets()` function we call `mfix::intersect_ls_walls()`.

   This performs an intersection operation with the level-set representing a

   wall at each MI.

2. Box geometries and regular geometries are comprised entirely out of planar

   surfaces. Therefore the levelset is not construction out of an EB factory (as

   would be the case for all other geometries). But out of an intersection with

   all planar surfaces. This has the advantage of correctly describing corners.

Fluid Reconstruction

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

The reconstruction algorithm is called whenever a cell in the particle's

neighbor stencil is covered. For no-slip walls, the reconstructed velocity in

that cell is linearly extrapolated from the nearest "valid" fluid cell and 0 at

the wall. This way the fluid velocity is consistent with the no-slip boundary

condition along the normal to the EB. For a planar EB wall, the following would

be enough (the level-set is called :fortran:`phi` here):

.. highlight:: fortran

::

   if ( is_covered_cell(flags(i,j,k))                         .and. &

   &   minval(abs(phi(i:i+1,j:j+1,k:k+1))) <= phi_threshold ) then

       ! Coordinates of cell center

       x_cc = ( real([i,j,k],rt) + half ) * dx

       ! Get phi at cell center

       call amrex_eb_interp_levelset(x_cc, x0, n_refine, phi, phlo, phhi, dx, phi_cc)

       ! Get normal at cell center

       call amrex_eb_normal_levelset(x_cc, x0, n_refine, phi, phlo, phhi, dx, norm_cc)

       ! Initial guess of interpolation point:

       x_i  = x_cc + two * abs(phi_cc) * norm_cc

       ! Get phi at interpolation point

       call amrex_eb_interp_levelset(x_i, x0, n_refine, phi, phlo, phhi, dx, phi_i)

       ! Compute interpolated velocity at x_i

       vel_i = trilinear_interp(vel_in, vilo, vihi, 3, x_i, x0, dx)

       ! Since interpolation point is only slightly shifted with respect to

       ! the mirror point, we approximate vel at mirror point with vel_i and

       ! then use linear interpolation between x_m and x_c

       vel_out(i,j,k,:) = vel_i * phi_cc / phi_i

If the EB represents a curved wall, the initial normal is not a good estimate

for the normal at the closest point on the wall. Therefore we start a the

covered cell, and "walking" along the EB normal on cell at a time (computed from

the level-set function), until the neighbor stencil does not include covered

cells:

.. highlight:: fortran

::

   ! Find location of interpolation point by iteration if necessary

   iter = 0

   find_xi: do

       if ( interp_stencil_is_valid(x_i, x0, dx, flags, flo, fhi) ) exit find_xi

       ! Get normal at interpolation point

       call amrex_eb_normal_levelset(x_i, x0, n_refine, phi, phlo, phhi, dx, norm_i)

       x_i = x_i + maxval(dx) * norm_i

       iter = iter + 1

       if ( iter > max_iter ) &

           call amrex_abort("reconstruct_velocity(): cannot find interpolation point")

   end do find_xi

Note that the level-set here needs to be at the same resolution as the fluid.

This is the reason why we need to keep the coarse level :cpp:`level_sets[0]`

even when running in single-level mode.

.. _AMReX EB documentation: https://amrex-codes.github.io/amrex/docs_html/EB_Chapter.html

.. _AMReX Level-Set documentation: https://amrex-codes.github.io/amrex/docs_html/EB.html#level-sets

.. _AMReX geometry documentation: https://amrex-codes.github.io/amrex/docs_html/EB.html#initializing-the-geometric-database 

   Inputs

   Fluids

   Particles

   EB

Notice

------