Efficient Time-Stepping Procedures for Miscible Displacement Problems in Porous Media.

Abstract

A model system of equations which has been used to describe the miscible displacement of one incompressible fluid by another in a porous medium is the coupled quasilinear system. Iteractive methods are presented and analyzed which are based on using a preconditioned conjugate gradient iteration for approximately solving the systems of linear equations produced at each time step by Galerkin methods for time-stepping the above system. Optimal order convergence rates are obtained for the iterative methods. The iterative methods are computationally more efficient than Galerkin methods previously proposed to solve the above system. The use of different time increments in the time-stepping procedures for the different variables is also presented and analyzed. The use of unequal time increments takes advantage of different smoothnesses in time of the physical variables p and c and greatly reduces the work done in the computation of the approximate solution.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1979
Accession Number
ADA070194

Entities

People

  • Richard E. Ewing

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Approximation (Mathematics)
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Computations
  • Convergence
  • Differential Equations
  • Displacement
  • Equations
  • Errors
  • Galerkin Method
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • New York
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)