Description of Variables

Principal Variables

The STOMP simulator has been designed with the principal variables defined in common blocks, which are included in nearly all subroutines. This approach reduces the number of arguments that are passed between routines and increases the readability of the code, because variable names remain unchanged between routines.

A list of common variables can be found here.

Field Variables

Field variables are defined at node points and are represented with two-dimensional arrays. 

Examples of field variables include:

• primary unknowns, saturation properties, rock/soil properties, and thermo­dynamic properties (e.g., temperature, pressure, phase saturation, porosity, density, and viscosity). 

The first index of a field variable indicates the time step or increment status. 

The second index of a field variable indicates the node number. The dimension of the first index depends on the operational mode or equivalently number of coupled flow equations; where the dimension will equal the number of unknowns plus two. Therefore, field variables at each node comprise a number of elements equal to the number of unknowns plus two. Each element for each field variable contains a variant on the field variable. For example, the first element or index contains the value of the field variable at the previous time step. A list of field variable variants is shown in Table 1.

Table 1. Field Variable Indexing Scheme

The primary variable order and corresponding field variable variant indexing depend on the opera­tional mode. However, primary variables are always ordered, regardless of the operational mode, according to the following equation sequence: energy, water mass, unique component masses to the operational mode, and salt mass. The primary variable ordering system for each operational mode is listed in Table 2. Primary variables are referred to by equation in Table 2, because primary variables for a given equation and operational mode are dependent on the local phase condition. Refer to the STOMP Theory Guide (White and Oostrom, 2000) for a description of primary variables, phase conditions, and variable switching. Consider an example for the STOMP-WA (Water-Air) Operational Mode, which solves the water mass and air mass conservation equations. For this operational mode, there would be four field variable variant indices. Using the aqueous saturation for an unsaturated node as the example field variable, the following variant definitions would apply: the first index would refer to the aqueous saturation at the previous time step, the second index would refer to the aqueous saturation at the current iteration or time step value, the third index would refer to the aqueous saturation with the aqueous pressure incremented, and the fourth index would refer to the aqueous saturation with the gas pressure incremented.

Table 2.  Primary Variable Sequencing Scheme

Flux variables

Flux variables are defined on node surfaces between node points or on boundary surfaces and are represented with two dimensional arrays. Examples of flux variables include heat fluxes, Darcy phase velocities, and component diffusion/dispersion fluxes. Flux variables are aligned with one of the primary orthogonal coordinate directions. Flux variables names that begin with the character 'U' are aligned with the x- or radial-direction coordinate, those which begin with the character 'V' are aligned with the y- or azimuthal-direction coordinate, and those which begin with the character 'W' are aligned with the z‑direction coordinate. The first index of a flux variable indicates the increment status and the second index indicates the surface number. Unlike field variables, previous time-step fluxes are not stored. Surface numbers do not correspond directly to node numbers. The number of surfaces in any given coordinate direction equals the number of nodes in that direction plus one.

A list of the flux variable variants is shown in Table 3. The primary variable order and corre­sponding field variable variant index depend on the operational mode. In Table 3, the upper node refers to the node in the east, north, or top direction (positive x-, y-, or z-direction) with respect to the surface. Likewise, the lower node refers to the node in the west, south, or bottom direction (negative x-, y-, or z‑direction) with respect to the surface. Consider an example for the STOMP-WA (Water-Air) Opera­tional Mode, which solves the water mass and air mass conservation equations. For this operational mode, there would be five flux variable variant indices. Using the z-direction aqueous Darcy velocity for an unsaturated node as the example field variable, the following variant definitions would apply: the first index would refer to the aqueous Darcy velocity for the current iteration or time step value, the second and third indices would refer to the Darcy velocity with the aqueous pressure in the “top” and “bottom” nodes incremented, respectively; and the fourth and fifth indices would refer to the Darcy velocity with the gas pressure in the “top” and “bottom” nodes incremented, respectively.

Table 3. Flux Variable Indexing Scheme

 

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