**RSICC CODE PACKAGE PSR-438**

**1. NAME AND TITLE**

POLYRES: Richards Equation Solver; Rectangular Finite Volume Flux Updating Solution.

**2. CONTRIBUTORS**

Pacific Northwest Laboratory, Richland, Washington, through the Energy Science and Technology Software Center, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 77; Many computers (P00438MNYC00).

**4. NATURE OF PROBLEM SOLVED**

POLYRES solves the transient, two-dimensional, Richards equation for water flow in unsaturated-saturated soils. The package is specifically designed to allow the user to easily model complex polygon-shaped regions. Flux, head, and unit gradient boundary conditions can be used. Spatial variation of the hydraulic properties can be defined across individual polygon-shaped subdomains, called objects. These objects combine to form a polygon-shaped model domain. Each object can have its own distribution of hydraulic parameters. The resulting model domain and polygon-shaped internal objects are mapped onto a rectangular, finite-volume, computational grid by a preprocessor. This allows the user to specify model geometry independently of the underlying grid and greatly simplifies user input for complex geometries. In addition, this approach significantly reduces the computational requirements since complex geometries are actually modeled on a rectangular grid. This results in well-structured, finite difference-like systems of equations that require minimal storage and are very efficient to solve.

**5. METHOD OF SOLUTION**

POLYRES uses a finite-volume approach on a rectangular grid to solve the Richards equation. Nonuniform grid discretization is allowed. A preconditioned conjugate gradient solver with an incomplete LDL preconditoner solves the set of linear algebraic equations defining the pressure head. To enhance global mass balance, the flux updating scheme of Kirkland et al. (1992) is used to update water content and pressure head at the end of each time step. The van Genuchten water retention and unsaturated hydraulic conductivity relationships are used.

**6. RESTRICTIONS OR LIMITATIONS**

A Fortran compiler is required. Memory allocation to arrays is carried out through PARAMETER and INCLUDE statements. Users will be limited only by their available memory. Users must be familiar with Fortran programming to complete the required user subroutines.

**7. TYPICAL RUNNING TIME**

POLYRES can solve problems that are very simple as well as those that are complex. Time requirements to solve any particular problem cannot be specified; experience suggests that POLYRES is comparable or better than other similar codes.

**8. COMPUTER HARDWARE REQUIREMENTS**

There are no inherent hardware requirements of POLYRES. Hardware requirements (cpu and memory) depend on the particular problem being solved.

**9. COMPUTER SOFTWARE REQUIREMENTS**

POLYRES requires a Fortran compiler. The source codes are independent of the operating system. It was initially submitted to ESTSC in 1995 then translated to RSICC and rereleased in January 2002. The software was run successfully at RSICC on an IBM RS/6000 under AIX 4.2.1 with the XL Fortran 5.1.1.0 compiler.

**10. REFERENCES**

R.G. Hills, P.D. Meyer, and M.L. Rockhold, "POLYRES: A Polygon-Based Ricards Equation Solver," NUREG/CR-6366 (December 1995).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and one DS/HD diskette which contains the Fortran source codes, test cases and documentation files.

**12. DATE OF ABSTRACT**

January 2002.

** KEYWORDS:** COMPLEX GEOMETRY; LIQUID PATHWAY; NUCLIDE TRANSPORT