Higher order Godunov methods for general systems of hyperbolic conservation laws
Journal of Computational Physics
Algorithms in C
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Journal of Computational Physics
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
A Crosswind Block Iterative Method for Convection-Dominated Problems
SIAM Journal on Scientific Computing
An Implementation of Tarjan's Algorithm for the Block Triangularization of a Matrix
ACM Transactions on Mathematical Software (TOMS)
Fully implicit discontinuous finite element methods for two-phase flow
Applied Numerical Mathematics
Monotonicity of control volume methods
Numerische Mathematik
A mass-conservative switching algorithm for modeling fluid flow in variably saturated porous media
Journal of Computational Physics
Domain decomposition strategies for nonlinear flow problems in porous media
Journal of Computational Physics
Hi-index | 31.46 |
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.