Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 227, Issue 24, Pages 10108-10124Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2008.08.024
Keywords
Porous media flow; Implicit upwind scheme; Topological sorting
Funding
- Research Council of Norway [1391441431, 158908/130]
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We present a family of implicit discontinuous Galerkin schemes for purely advective multiphase flow in porous media in the absence of gravity and capillary forces. To advance the solution one time step, one must solve a discrete system of nonlinear equations. By reordering the grid cells, the nonlinear system can be shown to have a lower triangular block structure, where each block corresponds to the degrees-of-freedom in a single or a small number of cells. To reorder the system, we view the grid cells and the fluxes over cell interfaces as vertices and edges in a directed graph and use a standard topological sorting algorithm. Then the global system can be computed by processing the blocks sequentially using a standard Newton-Raphson algorithm for the degrees-of-freedom in each block. Decoupling the system offers greater control over the nonlinear solution procedure and reduces the computational costs, memory requirements, and complexity of the scheme significantly. In particular, the first-order version of the method may be at least as efficient as modern streamline methods when accuracy requirements or the dynamics of the flow allow for large implicit time steps. (C) 2008 Elsevier Inc. All rights reserved.
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