Dissipation-based continuation method for multiphase flow in heterogeneous porous media

  title={Dissipation-based continuation method for multiphase flow in heterogeneous porous media},
  author={Jiamin Jiang and Hamdi A. Tchelepi},
  journal={J. Comput. Phys.},

Smooth Implicit Hybrid Upwinding for Compositional Multiphase Flow in Porous Media

Smooth Formulation for Multi-component Compositional Simulation with Superior Nonlinear Convergence

Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly

Efficient Localized Nonlinear Solution Strategies for Unconventional-Reservoir Simulation with Complex Fractures

An a-priori method to exploit the locality, based on the diffusive character of the Newton updates of pressure, that takes advantage of locality on timestep and Newton iteration levels to achieve significant computational speedup.

An Efficient Localized Nonlinear Solver for Simulating Natural Depletion of Unconventional Reservoirs with Complex Fracture Networks

Simulating unconventional reservoirs efficiently and accurately poses a big challenge. Transient flow can last for a long period and sharp solution gradients appear because of the severe

Upwinding and artificial viscosity for robust discontinuous Galerkin schemes of two-phase flow in mass conservation form

The modified DG method with artificial viscosity is demonstrated on a two-phase flow problem with heterogeneous rock permeabilities, where the high-order discretizations significantly outperform a conventional first-order approach in terms of computational cost required to achieve a given level of error in an output of interest.

Comparison of nonlinear field-split preconditioners for two-phase flow in heterogeneous porous media

The results demonstrate that the two-step nonlinear preconditioning approach— and in particular, FSMSN—results in a faster outer-loop convergence than with the SFI and FIM methods.



Analysis of Hybrid Upwinding for Fully-Implicit Simulation of Three-Phase Flow with Gravity

An Implicit Hybrid Upwinding (IHU) scheme for hyperbolic conservation laws is presented, extending the work of Lee, Efendiev, and Tchelepi to an arbitrary number of fluid phases and it is shown that the numerical flux obtained with the IHU is consistent, and a monotone function of its own saturation.

Convergence of Implicit Monotone Schemes with Applications in Multiphase Flow in Porous Media

An alternate, constructive proof is obtained that such schemes are well-defined and converge to the entropy solution of the conservation law for arbitrary CFL numbers for one-dimensional problems.

Domain decomposition strategies for nonlinear flow problems in porous media

Adaptively Localized Continuation-Newton Method—Nonlinear Solvers That Converge All the Time

Summary Growing interest in understanding, predicting, and controlling advanced oil-recovery methods emphasizes the importance of numerical methods that exploit the nature of the underlying physics.

Artificial Dissipation Models for the Euler Equations

Various artificial dissipation models that are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability, and convergence rates. In