MPI-AMRVAC  3.0 The MPI - Adaptive Mesh Refinement - Versatile Advection Code
Auxiliary variables (nw...)

# List of auxiliary variables

This document describes the differences and the intended use of the nwaux, nwextra parameters. These global parameters are defined in the mod_variables.t

## nw

This global parameter sets the total number of variables, determining the (last dimension-independent) size of the w(ixG^T,1:nw) array, and is always

 nw = nwflux+nwaux+nwextra


The idea is that there are nwflux conservative variables for which corresponding fluxes are defined in the physics modules, and that we have in addition a set of nwaux auxiliary variables, together with some extra nwextra variables. For these latter two types of variables, one does not have a corresponding flux definition in getflux, gefluxforhllc subroutines, and they also have no boundary conditions imposed on them.

## nwflux

The first 1:nwflux variables should be the conservative variables of the physics module at hand, and these are the ones that are updated by means of fluxes across cell boundaries, and are influenced by source terms (geometric or real physical source terms). Also, those variables change their meaning/content in the subroutines phys_to_primitive, phys_to_conserved. These two subroutines are thus switching from conservative to primitive and vice versa at appropriate places in the code. For the first 1:nwflux variables, the boundary conditions are to be imposed and existing boundary types have to be provided (like symm, asymm, special, cont, periodic, ...) in the par-file. For steady-state computations, the residual is based on only the temporal variation of these 1:nwflux variables.

## nwaux

When for the physics module at hand, one has nwaux>0, the slots in the w- array corresponding to nwflux+1:nwflux+nwaux contain so-called auxiliary variables. They can be computed directly from instantaneous local values of the flux 1:nwflux variables. These local auxiliary variables are all to be computed in the getaux subroutine in the physics module. Since they are to be used for facilitating flux specifications, they also need to be known in the ghost cells. This is taken care of by the fix_auxiliary call in the boundary condition treatment: note that they are thus computed from local (ghostcell) values from conservative variables (themselves computed according to their boundary type), so that we do not need to specify a boundary type for the nwflux+1:nwflux+nwaux variables. The local auxiliaries can in fact also be used to trigger refinement or coarsening. The current (Newtonian) physics modules of AMRVAC have no real use for these auxiliary variables.

## nwextra

An extra set of nwextra variables can be defined in addition to the presently available ones in physics modules by using the function var_set_extravar (from mod_variables.t) in usr_init of mod_usr.t. Like auxiliaries, they are not advanced (no fluxes need to be defined for them in get_flux), there are no boundary conditions imposed on them, and they should not be used for basing refinement/derefinement on. They are not computed in the ghost cells, and they can be used to store additional physical variables like old pressure or temperature values, the accumulated luminosity (internal energy change) during a timestep, local variables that depend on gradients of the flux variables (divergence of the velocity, curl of the magnetic field), etc. they need to be computed/updated in the pointed usr_process_grid subroutine. They work to facilitate the understanding of simulation processes.

## nwauxio

Only for post-processing purposes on saved snapshots from the code, one may want to compute additional auxiliary variables for visualization. Hence, only at the convert-stage (from .dat data file to any of the available formats in the convert subroutine in src/amrvacio/convert.t file) do we need to enlarge the data size from nw to nw+nwauxio, and their calculation is to be done in the pointed usr_aux_output subroutine, for which the default interface is given in the mod_usr_methods.t module. Correspondingly, the names have to be given in the pointed usr_add_aux_names subroutine strings. This means that normally nwauxio=0, but it can be at convert stage set to a nonzero value in the filelist part of the par- file.