STOMP

Solution Control Card Options (W)

For STOMP-W, three classes of options are specified via the Solution Control Card:

  1. Execution Mode Options - used to specify the state of the simulation.
  2. Operational Mode Options - used to specify the solved equations and active processes.
  3. Interfacial Averaging Options - used to specify the model for computing state variables at the centroids of grid-cell surfaces.

Execution Mode Options

Two Execution Modes are recognized: Normal, and Restart. In the Normal mode, initial state conditions are declared through the Initial Conditions Card. In the Restart mode, initial state conditions are assigned via a restart file from a previous execution or declared through the Initial Conditions Card, using the special overwrite option for selected parameters. Unless specified through the Output Control Card, restart files (i.e., restart.n) are generated at each plot.n write event, and have name extensions that correspond to the generating time step (e.g., the file restart.0028 would have been generated at the conclusion of time step 28). Restart files are text files that contain simulation time and control information, and a collection of field variables needed to redefine the simulation state for the operational mode. 

Execution Mode Options

Normal Mode

In the Normal mode, STOMP executes from a declared start time, using an initial state declared through the Initial Conditions Card, until the declared stop time or the declared number of time steps is reached, or an execution error or a sequence of convergence failures occur. The following keywords may also be used after specifying the "Normal" Execution Mode.

No Flow

This option results in the coupled flow and transport equations being computed only once, eliminating the flow calculations at each time step for a solute or reactive transport problem with a steady flow field. 

 

Restart Mode

In the Restart mode, STOMP executes from either a declared start time or the start time specified in the restart file, using an initial state defined by a previous execution, until the declared stop time or the declared number of time steps is reached, or an execution error or a sequence of convergence failures occur. The following keywords may be used after specifying the "Restart" Execution Mode.

File

This option triggers STOMP to read an additional character string, which is the name of the restart file.

No Flow

This option results in the coupled flow and transport equations being computed only once, eliminating the flow calculations at each time step for a solute or reactive transport problem with a steady flow field. 

Info

Overwrite 

When the keyword "overwrite" is included in the initial or boundary conditions cards with any of the above options during a restart simulation, the specified values will overwrite those from the restart file.

Operational Mode Options

The Operational Mode is STOMP-W and this solves the equation for water mass. This identifier is used to make certain that the operational mode of the STOMP executable matches the operational mode declared in the input file. The solved coupled equations, activation of solute transport, and reactive species transport is specified via keyword modifiers to the operational mode. Models for transporting passive solutes and reactive species are controlled via additional keyword modifiers to the operational mode. For example, solute transport is solved using the Patankar method, unless the keywords TVD or Roe Superbee also appear.

Operational Mode Options

Water or H2O or STOMP-W

 

Info

Accepted Keywords

One of the above keywords are required, and all are recognized for specifying the operational mode as STOMP-W

Additional options can be specified via keyword modifiers in the Operational Mode.
Operational Mode Modifiers

Transport

This modifier activates solute transport. By default, solute transport is solved using the Patankar (1980) method. Solution of the solute transport equation depends on the local Peclet number, which represents the ratio of advective transport to diffusive-dispersive transport. The power law scheme is based on the solute concentration profile for steady conditions with no sources nor decay. For a Peclet number of zero, diffusion-dispersion transport dominates and a linear profile of solute concentration occurs between two spatial points. For a Peclet number of one, advection and diffusion-dispersion equally contribute to solute transport and the solute concentration profile will be skewed towards an upstream solute concentration. For large Peclet numbers, advection transport dominates and the upstream solute concentration defines the solute concentration profile between two spatial points. The power- law scheme closely approximates the exact solution for steady conditions without excessive computational expense. Solute flux from combined advective and diffusive-dispersive transport can be expressed using the power-law scheme. See Patankar (1980) for more details.

 

Additional Transport Modifiers

Patankar

This is the default method and can also be optionally specified.

First-Order Upwind

The simplest upwind scheme possible is the first-order upwind scheme, which uses a finite difference stencil to simulate the direction of flow.

Leonard-TVD Scheme

This third-order scheme using a total variation diminishing (TVD) technique (Datta Gupta et al. 1991) is most appropriate for advection-dominated flow (high Peclet numbers). Conventional techniques, like the one discussed by Patankar (1980), suffer from artificial diffusion that smears otherwise sharp fronts. The smearing is a result of the first-order approximation of the advective term in the transport equation. Datta Gupta et al. (1991) proposed and successfully tested a third-order differencing scheme with an appropriate flux limiting function which significantly minimizes numerical diffusion, while, at the same time, avoids oscillations that commonly affect classical higher-order schemes.

Roe Superbee

All first order schemes suffer from artificial diffusion and all second order schemes suffer from dispersion, which creates oscillations around any discontinuities. Flux-limiter methods switch between a second order approximation when the region is smooth and a first order approximation when near a discontinuity. The Superbee limiter applies the minimum limiting and maximum steepening possible to remain TVD. 

Electrolyte

Corrects the aqueous liquid density and viscosity for electrolyte solute concentration.

Courant

Courant-Number Limited Transport

A dimensionless number that is used to characterize the relative extent of numerical oscillations in the numerical solution. The Courant Number is associated with the time discretization, and is calculated by multiplying cell velocity by the time step, and dividing that quantity by the distance. Given a certain spatial discretization, the time step must be selected such that the Courant number remains less than or equal to 1, or to some other user-specified value.

Vadose Courant

Vadose Zone Courant-Number Limited Transport

This option limits the application of the Courant number to the unsaturated cells in the domain. For a given a certain spatial discretization, the time step calculation will be determined such that the Courant number remains less than or equal to 1 or some other user-specified value, in the unsaturated zone.

 

ECKEChem

This modifier activates reactive species transport. The reactive transport algorithms use the same transport schemes as the solute transport model, and therefore are controlled through the keyword options TVD and Roe Superbee.

 

Additional ECKEChem Modifiers

Transport

Used to specify that non-reactive solutes are also to be simulated.

Patankar

This is the default method and can be optionally specified.

First-Order Upwind

The simplest upwind scheme possible is the first-order upwind scheme, which uses a finite difference stencil to simulate the direction of flow.

Leonard-TVD Scheme

This third-order scheme using a total variation diminishing (TVD) technique (Datta Gupta et al. 1991) is most appropriate for advection-dominated flow (high Peclet numbers). Conventional techniques, like the one discussed by Patankar (1980), suffer from artificial diffusion that smears otherwise sharp fronts. The smearing is a result of the first-order approximation of the advective term in the transport equation. Datta Gupta et al. (1991) proposed and successfully tested a third-order differencing scheme with an appropriate flux limiting function which significantly minimizes numerical diffusion, while, at the same time, avoids oscillations that commonly affect classical higher-order schemes.

Roe Superbee

All first order schemes suffer from artificial diffusion and all second order schemes suffer from dispersion, which creates oscillations around any discontinuities. Flux-limiter methods switch between a second order approximation when the region is smooth and a first order approximation when near a discontinuity. The Superbee limiter applies the minimum limiting and maximum steepening possible to remain TVD. 

Courant

Courant-Number Limited Transport

A dimensionless number that is used to characterize the relative extent of numerical oscillations in the numerical solution. The Courant Number is associated with the time discretization, and is calculated by multiplying cell velocity by the time step, and dividing that quantity by the distance. Given a certain spatial discretization, the time step must be selected such that the Courant number remains less than or equal to 1, or to some other user-specified value.

Vadose Courant

Vadose Zone Courant-Number Limited Transport

This option limits the application of the Courant number to the unsaturated cells in the domain. For a given a certain spatial discretization, the time step calculation will be determined such that the Courant number remains less than or equal to 1 or some other user-specified value, in the unsaturated zone.

Equilibrium Reduced

With this option, the equilibrium aqueous speciation reactions are decoupled from the kinetic reactions. This can improve convergence and decrease run times.

Minimum Concentration

This option is a numerical control that allows for the specification of the minimum aqueous concentration for all species in the simulation.

Log

Since concentrations of species are positive and because mass action laws in chemistry involve products and powers, logarithms of concentrations can be used to solve the geochemical reaction equations.

Guess

This option can be used to establish the initial concentrations within the simulation domain. This routine is called once during the initialization routine.

Porosity Alteration with Precipitation

As minerals precipitate and dissolve, the new mineral volumes are used to calculate changes in porosity for the porous medium.

Effective Reaction Area

This option will scale the mineral reaction area based on the water saturation of the cell.

Constant Surface Area 

Mineral surface areas remain unchanged by precipitation and dissolution reactions. Mineral surface areas are always maintained at the initial value.

Warning

ECKEChem

Using this keyword requires the ECKEChem Module to be implemented in the simulator. When using Operational Mode Modifiers for Reactive Transport, include the keyword "transport" only when solutes are also being simulated. For example, for geochemical reactive species only, "Eckechem w/ TVD" might be specified. If non-geochemical species are simulated, then "Eckechem w/ Transport w/ TVD would be specified.

Interfacial Averaging Options

State variables at the centroids of grid-cell surfaces are required to compute fluxes between grid-cell centroids. Models for computing the state variables on grid-cell surfaces are referred to as interfacial averaging schemes and use the state variables at adjacent grid-cells to compute the surface variables. Default interfacial averaging schemes or various variable types have been selected for STOMP. Schemes other than the defaults can be specified.

Interfacial Averaging Schemes

Field variables, which include physical, thermodynamic, and hydrologic properties, are defined in the finite-difference formulation at the node centers. Conversely, flux variables are defined at node interfaces. Computation of flux variables requires knowledge of field variables at node interfaces. Values of flux variables at node interfaces are evaluated by averaging the field values for the two nodes adjoining an interfacial surface. Interfacial averaging schemes may be declared individually for each field variable through the Interfacial Averaging Variables input.

The default interfacial averaging schemes for the simulator are shown in the Table below. For simulations of physical systems involving heat transfer, it should be noted that convergence problems might arise if the density properties are not averaged with upwind weighting. Likewise, infiltration problems typically demonstrate strong dependencies on the relative permeability of the infiltrating fluid.

Field Variable

Default Interfacial Averaging

 

Aqueous Density

Upwind 

Aqueous Relative Permeability

Upwind 

Aqueous Viscosity

Harmonic

Hydraulic Dispersion

Harmonic

Intrinsic Permeability

Harmonic

Solute Diffusion

Harmonic

References: 

Datta-Gupta, A, LW Lake, GA Pope, and K Sepehnoori. 1991. High-Resolution Monotonic Schemes for Reservoir Fluid Flow Simulation.  In Situ, 15(3):289-317.

Patankar, SV. 1980. Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, Washington, D. C.

Poeter, EP and MC Hill. 1998. Documentation of Ucode: A Computer Code for Universal Inverse Modeling, 98-4080, USGS Water-Resources Investigations Report.

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