Adaptive Mesh Refinement and Multilevel Iteration for Flow in Porous Media

Hornung, Richard D.; Trangenstein, John A.

doi:10.1006/jcph.1997.5779

Cited by 76 publications

(55 citation statements)

References 53 publications

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“…These applications include single-phase flow in heterogeneous porous media (Cao and Kitanidis, 1999), unsaturated flow (Li et al, 2007), multispecies reactive transport (Wolfsberg and Freyberg, 1994), coupled density-dependent flow and transport (Trompert, 1993;van Esch, 2002), and multiphase flow and multicomponent transport (Hornung and Trangenstein, 1997;Pau et al, 2008). All these applications are limited to capability demonstration.…”

Section: Actual Phase I Accomplishmentsmentioning

confidence: 99%

COUPLING STATE-OF-THE-SCIENCE SUBSURFACE SIMULATION WITH ADVANCED USER INTERFACE AND PARALLEL VISUALIZATION: SBIR Phase I Final Report

Hardeman¹,

Swenson²,

Finsterle³

et al. 2008

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Executive SummaryThis is a Phase I report on a project to significantly enhance existing subsurface simulation software using leadership-class computing resources, allowing researchers to solve problems with greater speed and accuracy. Subsurface computer simulation is used for monitoring the behavior of contaminants around nuclear waste disposal and storage areas, groundwater flow, environmental remediation, carbon sequestration, methane hydrate production, and geothermal energy reservoir analysis. The Phase I project was a collaborative effort between Thunderhead Engineering (project lead and developers of a commercial pre-and post-processor for the TOUGH2 simulator) and Lawrence Berkeley National Laboratory (developers of the TOUGH2 simulator for subsurface flow). The Phase I project successfully identified the technical approaches to be implemented in Phase II.

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Section: Actual Phase I Accomplishmentsmentioning

confidence: 99%

COUPLING STATE-OF-THE-SCIENCE SUBSURFACE SIMULATION WITH ADVANCED USER INTERFACE AND PARALLEL VISUALIZATION: SBIR Phase I Final Report

Hardeman¹,

Swenson²,

Finsterle³

et al. 2008

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“…Structured grids with patches of refinement have been used for time dependent and time independent problems in applications such as fluid flow [3], [8], [10], [12], electromagnetics [11], [14], [17], [21], and plasma physics [6], [18]. The missing values of the solution at the interfaces are determined by interpolation.…”

Section: Introductionmentioning

confidence: 99%

Accurate and stable grid interfaces for finite volume methods

Ferm

Lötstedt

2004

Applied Numerical Mathematics

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A convection-diffusion equation is discretized by a finite volume method in two space dimensions. The grid is partitioned into blocks with jumps in the grid size at the block interfaces. Interpolation in the cells adjacent to the interfaces is necessary to be able to apply the difference stencils. Second order accuracy is achieved and the stability of the discretizations is investigated. The interface treatment is tested in the solution of the compressible Navier-Stokes equations. The conclusions from the scalar equation are valid also for these equations.

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“…Our approach is similar to the approach introduced by Hornung & Trangenstein (1997) and to the approach discussed by Propp (1998). In these approaches, the solution is represented on a hierarchical sequence of nested grids with successively finer spacing in both time and space.…”

Section: Introductionmentioning

confidence: 99%

“…The method presented here uses subcycling in time so that all levels are advanced at the same Courant-Friedrichs-Levy (CFL) number, thus reducing the numerical dissipation of the explicit upwind advection scheme used to advance the solution. The major difference between the approach adopted here and that of Hornung & Trangenstein (1997) is that the current method does not require a global, multilevel pressure solve at each fine-grid time step. Instead, when advancing a given level, we solve the pressure on that level only with boundary conditions obtained from the coarser levels.…”

Section: Introductionmentioning

confidence: 99%

“…An alternative approach to local refinement is based on structured-grid adaptive mesh refinement (AMR). This type of approach, based on the strategy introduced for gas dynamics by Berger & Colella (1989), was first applied to porous media flow by Hornung & Trangenstein (1997) and by Propp (1998). Additional developments are discussed in the work by Trangenstein (2002), Trangenstein & Bi (2002) and Hoang & Kleppe (2006).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media

Pau

Almgren

Bell

et al. 2009

Phil. Trans. R. Soc. A.

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In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.

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Adaptive Mesh Refinement and Multilevel Iteration for Flow in Porous Media

Cited by 76 publications

References 53 publications

COUPLING STATE-OF-THE-SCIENCE SUBSURFACE SIMULATION WITH ADVANCED USER INTERFACE AND PARALLEL VISUALIZATION: SBIR Phase I Final Report

COUPLING STATE-OF-THE-SCIENCE SUBSURFACE SIMULATION WITH ADVANCED USER INTERFACE AND PARALLEL VISUALIZATION: SBIR Phase I Final Report

Accurate and stable grid interfaces for finite volume methods

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media

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