# The Flux Object¶

This page is intended to document the creation, use, and destruction of the Fluxes object in Enzo. This will not be a complete description of the Flux Correction algorithm, see the primary references for that.

## Purpose¶

In order to keep the change in zone size across grid boundaries consistent with the underlying conservation law, Flux Correction is used. Basically, it makes sure that the change in Total Energy inside a subgrid (or mass, momentum, or any other conserved quantitiy) is equal to the flux across the boundary as seen by both levels. This means that the coarse grid, which gets its solution in that space replaced by the fine grid data, also needs to have the zones right outside that space updated so they also see that same flux.

To facilitate this operation, the Fluxes object is used.

For each subgrid, there are two Fluxes objects, that store the flux computed in the solver (typically Grid_[xyz]EulerSweep). One stores the fluxes that the fine grid computes, and one stores the fluxes that the coarse grid computes. These are stored in two objects: a grid member fluxes BoundaryFluxes for the fine data, and fluxes ***SubgridFluxesEstimate for the coarse data.

## Fluxes.h¶

The actual object can be found in src/enzo/Fluxes.h.

struct fluxes
{
long_int LeftFluxStartGlobalIndex[MAX_DIMENSION][MAX_DIMENSION];
long_int LeftFluxEndGlobalIndex[MAX_DIMENSION][MAX_DIMENSION];
long_int RightFluxStartGlobalIndex[MAX_DIMENSION][MAX_DIMENSION];
long_int RightFluxEndGlobalIndex[MAX_DIMENSION][MAX_DIMENSION];
float *LeftFluxes[MAX_NUMBER_OF_BARYON_FIELDS][MAX_DIMENSION];
float *RightFluxes[MAX_NUMBER_OF_BARYON_FIELDS][MAX_DIMENSION];
};


This contains two sets of arrays for the actual flux values, and 4 arrays to describe the position of the flux in the computational domain. There is a flux on each face of the subgrid, and each flux has a vector describing its start and end. For instance, LeftFluxStartGlobalIndex[0][dim] describes the starting index for the X face left flux. LeftFluxes[densNum][0] describes the flux of density across the left x face.

## SubgridFluxesEstimate¶

SubgridFluxesEstimate is a 2 dimensional array of pointers to Fluxes objects that a given grid patch will fill. Its indexing is like *SubgridFluxesEstimate[Grid][Subgrid] , where Grid goes over all the grids on a level, and Subgrid goes over that grid’s subgrids PLUS ONE for the grid itself, as each grid needs to keep track of its own boundary flux for when it communicates with the parent. (This last element is used in conjunction with the BoundaryFluxes object, as we’ll see later)

### Allocation¶

Allocation of the pointer array for the grids on this level happens at the beginning of EvolveLevel:

fluxes ***SubgridFluxesEstimate = new fluxes **[NumberOfGrids];


At the beginning of the time loop, each grid has its subgrid fluxes array allocated, and a fluxes object is allocated for each subgrid (plus one for the grid itself)

while (dtThisLevelSoFar < dtLevelAbove) {
... timestep computation  ...
for (grid = 0; grid < NumberOfGrids; grid++) {

// The array for the subgrids of this grid
SubgridFluxesEstimate[grid] = new fluxes *[NumberOfSubgrids[grid]];

if (MyProcessorNumber ==
Grids[grid]->GridData->ReturnProcessorNumber()) {

for( Subgrids of grid ){
SubgridFluxesEstimate[grid][counter] = new fluxes;
... Setup meta data ...
}

/* and one for the grid itself */
SubgridFluxesEstimate[grid][counter] = new fluxes;
... and some meta data ...

}
} // end loop over grids (create Subgrid list)


Note that in older versions of Enzo are missing the processor check, so fluxes objects are allocated for each grid and subgrid on each processor, causing a bit of waste. This has been fixed since Enzo 1.5.

The LeftFluxes and RightFluxes are allocated in Grid_SolveHydroEquations.C

### Assignment¶

After the LeftFluxes and RightFluxes are allocated in Grid_SolveHydroEquations.C, they are filled with fluxes from the solver. In v2.0, the C++ and FORTRAN interface with the hydrodynamics solver was improved to avoid the previous method that juggled pointers to a temporary array for the fluxes returned from the FORTRAN hydro solver. Now Grid_[xyz]EulerSweep.C allocates memory for each of the flux variables and passes them into each of the FORTRAN hydro routines. This removes any size limitations that the old wrappers had when the temporary array was too large.

### Flux Correction¶

After being filled with coarse grid fluxes, SubgridFluxesEstimate is then passed into UpdateFromFinerGrids, where it is used to correct the coarse grid cells and boundary fluxes. For each grid/subgrid, SubgridFluxesEstimate is passed into Grid_CorrectForRefinedFluxes as InitialFluxes. The difference of InitialFluxes and RefinedFluxes is used to update the appropriate zones. (Essentially, the coarse grid flux is removed from the update of those zones ex post facto, and replaced by the average of the (more accurate) fine grid fluxes.

See the section below for the details of SubgridFluxesRefined and RefinedFluxes.

The last thing to be done with SubgridFluxesEstimate is to update the BoundaryFluxes object for each grid on the current level. Since multiple fine grid timesteps are taken for each parent timestep, the total flux must be stored on the grids boundary. This is done in Grid_AddToBoundaryFluxes, at the end of the EvolveLevel timestep loop.

### Deallocation¶

In the same grid loop that BoundaryFluxes is updated, the SubgridFluxesEstimate object is destroyed with DeleteFluxes, and the pointers themselves are freed.

for (grid = 0; grid < NumberOfGrids; grid++) {
if (MyProcessorNumber == Grids[grid]->GridData->ReturnProcessorNumber()) {

(SubgridFluxesEstimate[grid][NumberOfSubgrids[grid] - 1])

for (subgrid = 0; subgrid < NumberOfSubgrids[grid]; subgrid++) {

DeleteFluxes(SubgridFluxesEstimate[grid][subgrid]);

delete SubgridFluxesEstimate[grid][subgrid];
}
delete [] SubgridFluxesEstimate[grid];
}


## grid.BoundaryFluxes¶

Each instance of each grid has a fluxes BoundaryFluxes object that stores the flux across the surface of that grid. It’s used to correct it’s Parent Grid.

### Allocation¶

BoundaryFluxes is allocated immediately before the timestep loop in EvolveLevel by the routine ClearBoundaryFluxes.

### Usage¶

For each grid, BoundaryFluxes is filled at the end of the EvolveLevel timestep loop by the last element of the array SubgridFluxesEstimate[grid] for that grid. This is additive, since each grid will have multiple timesteps that it must correct its parent for. This is done by AddToBoundaryFluxes, as described above.

BoundaryFluxes is used in UpdateFromFinerGrids to populate another fluxes object, SubgridFluxesRefined. This is done in GetProjectedBoundaryFluxes. The values in SubgridFluxesRefined are area weighted averages of the values in BoundaryFluxes, coarsened by the refinement factor of the simulation. (So for factor of 2 refinement, SubgridFluxesRefined has half the number of zones in each direction than BoundaryFluxes, and matches the cell width of the parent grid.)

BoundaryFluxes is also updated from subgrids in CorrectForRefinedFluxes. This happens when a subgrid boundary lines up exactly with a parent grid boundary. However, in many versions of Enzo, this is deactivated by the following code:

        CorrectLeftBoundaryFlux = FALSE;
CorrectRightBoundaryFlux = FALSE;
#ifdef UNUSED
if (Start[dim] == GridStartIndex[dim]-1)
CorrectLeftBoundaryFlux = TRUE;
if (Start[dim] + Offset == GridEndIndex[dim]+1)
CorrectRightBoundaryFlux = TRUE;
#endif /* UNUSED */


It is unclear why this is, but removal of the UNUSED lines restores conservation in the code, and is essential for proper functioning of the MHD version of the code (which will be released in the future.) I have seen no problems from removing this code.

Many implementations of block structured AMR require a layer of zones between parent and subgrid boundaries. Enzo is not one of these codes.

### Deallocation¶

BoundaryFluxes is only deleted once the grid itself is deleted. This happens mostly in RebuildHierarchy.

## SubgridFluxesRefined¶

The final instance of a fluxes object is fluxes SubgridFluxesRefined. This object takes the fine grid fluxes, resampled to the coarse grid resolution, and is used to perform the flux correction itself. This section is short, as its existance has been largely documented in the previous sections.

### Allocation¶

SubgridFluxesRefined is declared in UpdateFromFinerGrids. The actual allocation occurs in Grid_GetProjectedBoundaryFluxes, where it’s passed in as ProjectedFluxes.

### Usage¶

SubgridFluxesRefined is also filled in Grid_GetProjectedBoundaryFluxes, as the area weighted average of the subgrid boundary flux.

It is then passed into Grid_CorrectForRefinedFluxes, Here, it is used to update the coarse grid zones that need updating.

### Deallocation¶

SubgridFluxesRefined is deleted after it is used in Grid_CorrectForRefinedFluxes.