Efficient Time-Stepping Procedures for Miscible Displacement Problems in Porous Media.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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.
- Numerical Mathematics