Accession Number:

ADA429158

Title:

Nonlinear Solvers for Subsurface Flow Problems

Descriptive Note:

Final progress rept. 1 May 1999-30 Apr 2002

Corporate Author:

NORTH CAROLINA STATE UNIV AT RALEIGH DEPT OF MATHEMATICS

Report Date:

2002-07-08

Pagination or Media Count:

8.0

Abstract:

The aims of this project are development of linear and nonlinear solvers and temporal integration methods in the context of 3D simulations of subsurface flow and transport. In the period covered by this report, the Principal Investigator and his students completed the initial phase of development of a two-level preconditioner, applied those results to unsaturated and multiphase flow problems, and derived condition number estimates. They also have applied their work on simulation to problems in optimal design. The project focused on numerical methods for solving linear and nonlinear equations and related problems in time-dependent simulations. The motivating application was simulation of flow through porous media, in particular the unsaturated zone in the subsurface. The nature of the nonlinearities and the physical properties of the equations make standard methods for solution of equations perform in ways not predicted by current theory. The objective was to understand these effects and design and analyze new solvers. By doing this the new solvers can be incorporated in production codes and adapt to changes in the solution as the simulation progresses. This ability to adapt is crucial to an efficient simulation. The basic research issues in nonlinear equation solvers arise from the nature of the nonlinearities. These do not have the smoothness properties that a traditional Newtons method code requires to converge in the usual way. The group performed research directed toward an understanding of how the nonlinearity can be approximated in a way that improves the performance of the solver and, at the same time, does not affect the accuracy of the simulation. The nonlinearities also affect the way in which the nonlinear solver and the time-dependent part of the simulator communicate. This communication is important for temporal adaptation. A list of 15 publications and conference presentations is included. 19 refs.

Subject Categories:

  • Geology, Geochemistry and Mineralogy
  • Hydrology, Limnology and Potamology
  • Numerical Mathematics
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE