To main content

An implicit local time-stepping method based on cell reordering for multiphase flow in porous media

An implicit local time-stepping method based on cell reordering for multiphase flow in porous media

Category
Journal publication
Abstract
We discuss how to introduce local time-step refinements in a sequential implicit method for multiphase flow in porous media. Our approach relies heavily on causality-based optimal ordering, which implies that cells can be ordered according to total fluxes after the pressure field has been computed, leaving the transport problem as a sequence of ordinary differential equations, which can be solved cell-by-cell or block-by-block. The method is suitable for arbitrary local time steps and grids, is mass-conservative, and reduces to the standard implicit upwind finite-volume method in the case of equal time steps in adjacent cells. The method is validated by a series of numerical simulations. We discuss various strategies for selecting local time steps and demonstrate the efficiency of the method and several of these strategies by through a series of numerical examples.
Language
English
Author(s)
Affiliation
  • SINTEF Digital / Mathematics and Cybernetics
  • TOTAL
Year
2020
Published in
Journal of Computational Physics: X
ISSN
2590-0552