Media Type#

Media Type = {model_name}

Description / Usage#

This card is used to designate the characteristic medium type for solid materials so that the proper microstructural features/models may be imposed. Basically, the choices are dictated by whether the medium is to be modeled as porous (viz. a medium in which flow will be determined relative to the motion of a porous solid skeleton) or as continuous (viz., in which the mechanics equations apply to all parts of the medium and not weighted by a solid fraction). If porous flow through Darcy or Brinkman formulations are desired in the material, then the phase is designated as continuous.

The input parameter is a {model_name} and has the following possible values:


{model_name} Name of the media model; the choices are







Specific characteristics of these types are identified below, including other cards that must be present.

  • If the type chosen is CONTINUOUS, then the material is assumed to be amorphous and no further microstructure properties need to be specified (next required card is the Diffusion Constitutive Equation).

  • In a porous medium with one phase in the pores (i.e. a saturated medium), use POROUS_SATURATED then only the Porosity and Permeability cards are required. A POROUS_SATURATED medium model enables the user to solve the simplest porous flow equation for the liquid phase pressure only for rigid porous media (see the porous_sat or porous_liq equation cards). For deformable porous saturated media, one can employ a stress balance and porosity equation for deformable porous media (see mesh* equation cards and porous_deform equation card).

  • In a porous medium with two phases in the pores (such as air-water, i.e., an unsaturated medium), two options exist - POROUS_UNSATURATED, a formulation of the porous flow problem using the capillary pressure as the field variable (gas pressure assumed to be uniform), and POROUS_TWO_PHASE, a formulation of the porous flow problem using the liquid pressure and gas pressure as field variables. All the cards in this Microstructure porous flow section, except the Brinkman cards (FlowingLiquid Viscosity and Inertia Coefficient), are needed for the unsaturated or two-phase models. As in the saturated case above, these options can also be chosen for deformable porous media, for which the Lagrangian mesh stress equations and the porosity equation are used to complete the effective stress principle formulation.

  • The POROUS_BRINKMAN model is an extension of the Navier-Stokes equation for porous media. In addition, it has an inertia term intended to account for boundary and interface deficiencies at Reynold’s numbers greater than one (Re > 1), a deficiency in all Darcy flow models (see, e.g., Gartling, et. al., 1996). It is a vector formulation (the momentum equations) of saturated flow in a porous medium which reduces to the Navier-Stokes equations as the porosity increases to one (φ → 1). For Brinkman flow, the input parameters (i.e., cards) that must be specified from this section are Porosity, Permeability, FlowingLiquid Viscosity, and Inertia Coefficient. Please note the use of two viscosities; for the Brinkman media type, the viscosity entered via the (Mechanical Properties and Constitutive Equations) Viscosity card is interpreted to be the Brinkman viscosity (μB) and is used to calculate the viscous stresses (see Gartling, et. al., 1996) while the FlowingLiquid Viscosity (μ) is used in the correction term for nonlinear drag forces in porous media. Brinkman viscosity is an effective value and can be taken as the porosity weighted average of the matrix and fluid. It is generally not correct to set it equal to the liquid viscosity (Martys, et. al., 1994; Givler and Altobelli, 1994).

  • The POROUS_SHELL_UNSATURATED model is used for thin shell, open pore, porous media, viz. the shell_sat_open equation. This media type instructs GOMA to obtain most of the media properties from the bulk continuum specifications just like POROUS_UNSATURATED. Exceptions are the Porous Shell Cross Permeability model and the Porous Shell Height material models. Please see the porous shell tutorial


Following is a sample card:


This card will require a plethora of material models for Darcy flow of liquid and gas in a porous medium. It also will require the use of two Darcy flow mass balances in the Problem Description EQ specification section, specifically porous_liq and porous_gas equations. See references below for details.

Technical Discussion#

In solving porous medium problems, it is important to understand that each conservation equation represents a component, or species balance. The porous_liq equation is actually a species balance for the liquid phase primary component (e.g. water) for all phases in the medium, viz. liquid, gas, and solid. This is the case even though the dependent variable is the liquid phase pressure. This is the only required equation for rigid POROUS_SATURATED media. The same holds true for rigid POROUS_UNSATURATED media, as the liquid solvent is present in liquid and gas vapor form (it is actually taken as insoluble in the solid). For deformable media, one must add a stress balance through the mesh* equations (in LAGRANGIAN form, as described on the Mesh Motion card) and a solid phase “solvent” balance which is used to solve for the porosity, viz. the porous_deform equation. In these cases, the gas is taken to be at constant pressure. If pressure driven Darcy flow is important in the gas, an additional species balance for the primary gas component is required through the porous_gas equation. This last case is the so-called POROUS_TWO_PHASE media type.

Options for representing the solid medium as rigid or deformable are discussed under the Saturation, Permeability and Porosity cards. When rigid porous media are modeled, both porosity and permeability are constant. In Goma 4.0, these concepts were being researched and improved, with much of the usage documentation residing in technical memos.


GT-008.2: Porous Media Capabilities/Tutorial for GOMA. User Guidance for Saturated Porous Penetration Problems, August 11, 1999, P. R. Schunk

GT-009.3: GOMA’s capabilities for partially saturated flow in porous media, September 1, 2002, P. R. Schunk

Gartling D. K., C. E. Hickox and R. C. Givler 1996. “Simulations of Coupled Viscous and Porous Flow Problems”, Comp. Fluid Dynamics, 7, 23-48.

Givler, R. C. and S. A. Altobelli 1994. “A Determination of the Effective Viscosity for the Brinkman-Forchheimer Flow Model.” J. Fluid Mechanics, 258, 355-370.

Martys, N., D. P. Bantz and E. J. Barboczi 1994. “Computer Simulation Study of the Effective Viscosity in Brinkman’s Equation.” Phys. Fluids, 6, 1434-1439