Showing papers by "Mary F. Wheeler published in 2002"
TL;DR: This methodology has been implemented in the Center for Subsurface Modeling's multiphysics multiblock simulator IPARS (Integrated Parallel Accurate reservoir Simulator), and it can be applied to non-matching grids across the interface, multinumerics and multiph physics models, and mortar adaptivity.
Abstract: In mortar space upscaling methods, a reservoir is decomposed into a series of subdomains (blocks) in which independently constructed numerical grids and possibly different physical models and discretization techniques can be employed in each block. Physically meaningful matching conditions are imposed on block interfaces in a numerically stable and accurate way using mortar finite element spaces. Coarse mortar grids and fine subdomain grids provide two-scale approximations. In the resulting effective solution flow is computed in subdomains on the fine scale while fluxes are matched on the coarse scale. In addition the flexibility to vary adaptively the number of interface degrees of freedom leads to more accurate multiscale approximations. This methodology has been implemented in the Center for Subsurface Modeling’s multiphysics multiblock simulator IPARS (Integrated Parallel Accurate reservoir Simulator). Computational experiments demonstrate that this approach is scalable in parallel and it can be applied to non-matching grids across the interface, multinumerics and multiphysics models, and mortar adaptivity. Moreover unlike most upscaling approaches the underlying systems can be treated fully implicitly.
130 citations
01 Jan 2002
TL;DR: A combined method consisting of the mixed finite element method for flow and the discontinuous Galerkin method for transport is introduced for the coupled system of miscible displacement problem.
Abstract: A combined method consisting of the mixed finite element method for flow and the discontinuous Galerkin method for transport is introduced for the coupled system of miscible displacement problem. A “cut-off” operator M is introduced in the discontinuous Galerkin formular in order to make the combined scheme converge. Optimal error estimates in L 2(H 1) for concentration and in L ∞(L 2) for velocity are derived.
108 citations
TL;DR: In this article, a new approach to discretizing flow in porous media via mixed finite element methods on non-matching multiblock grids is presented, where the velocity space along the interfaces is enhanced to give flux-continuous approximation.
Abstract: The paper presents a new approach to discretizing flow in porous media via mixed finite element methods on non-matching multiblock grids. The velocity space along the interfaces is enhanced to give flux-continuous approximation. No additional matching conditions need to be imposed. The computational complexity of the resulting algebraic problem is comparable to the one for the single-block case. A priori error estimates for the pressure and the velocity and numerical experiments confirming the theory are presented.
75 citations
TL;DR: This work overviews both basic and widely recognized multiphase and multicomponent models and presents several simulation examples which reflect the experiences of the research group at the Center for Subsurface Modeling at The University of Texas at Austin.
62 citations
TL;DR: This paper derives optimal {a priori} error estimates for mixed finite element displacement formulations of the acoustic wave equation with primary unknowns are pressure and the gradient of pressure.
Abstract: In this paper we derive optimal {a priori} $L^{\infty}(L^2)$ error estimates for mixed finite element displacement formulations of the acoustic wave equation. The computational complexity of this approach is equivalent to the traditional mixed finite element formulations of the second order hyperbolic equations in which the primary unknowns are pressure and the gradient of pressure. However, the displacement formulations with the physical variables of interest, displacement and pressure, requires less regularity on the displacement.
60 citations
TL;DR: The multiblock algorithm for an implicit black-oil model as implemented in the multiphase simulator framework of IPARS (Integrated Parallel Accurate Reservoir Simulator) is discussed and regularization techniques and preconditioners are proposed to improve the performance of the solver.
Abstract: In this paper we discuss the multiblock algorithm for an implicit black-oil model as implemented in the multiphase simulator framework of IPARS (Integrated Parallel Accurate Reservoir Simulator) The multiblock algorithm decomposes the simulation domain into multiple nonoverlapping subdomains, or blocks, according to the geometric, geological, and physical/chemical properties, and well distribution Each block can have its own grid system, and the grids of the neighboring blocks can be nonmatching on the interface, which allows for local grid refinement, or discrete fault or fracture modeling Adjacent blocks are coupled across the interface by a set of conditions imposing a continuity of both primary variables and component mass fluxes that is realized through the use of special interface mortar variables The resulting system is solved by an interface Newton procedure Regularization techniques and preconditioners are proposed to improve the performance of the solver The multiblock technique is effective and scalable, as shown by our numerical experiments In addition, we present how the multiblock black-oil model has been used in the coupling of different physical models
25 citations
TL;DR: In this article, the authors presented the coupling of two locally conservative methods for elliptic problems: namely, the discontinuous Galerkin method and the mixed finite element method, which can be defined with or without interface Lagrange multipliers.
Abstract: This work presents the coupling of two locally conservative methods for elliptic problems: namely, the discontinuous Galerkin method and the mixed finite element method. The couplings can be defined with or without interface Lagrange multipliers. The formulations are shown to be equivalent. Optimal error estimates are given; penalty terms may or may not be included. In addition, the analysis for non-conforming grids is also discussed.
16 citations
01 Jan 2002
TL;DR: A parallel computational portal IPARS for modeling multi-phase, multiphysics flow in porous media has been developed and allows coupling of different domains and models using either a mortar or dual formulation.
Abstract: A parallel computational portal IPARS for modeling multi-phase, multiphysics flow in porous media has been developed. IPARS allows coupling of different domains and models using either a mortar or dual formulation.
16 citations
01 Jan 2002
TL;DR: In this article, the multiblock approach in the integrated parallel accurate reservoir simulator (IPARS) is used to simulate the flow of biofilm growth in porous media at the pore scale and up scaling.
Abstract: Advanced techniques and algorithms for reservoir simulation, I: frontier issues in managin oil and gas production.- Advanced..., II: the multiblock approach in the integrated parallel accurate reservoir simulator (IPARS).- Advanced..., III: multiphysics coupling for two phase flow in degenerate conditions.- Advanced..., IV: multiblock solvers and preconditioners.- Upscaling of biological processes and multiphase flow in highly heterogeneous media.- Foamy oil flow in porous media.- Diffusion in deformable media.- Fractures, faults, and the nonlinear RTM dynamics of sedimentary basins.- Probability functionals, homogenization and comprehensive reservoir simulators.- Diffusion-limited contamination and decontamination in a layered aquitard: forensic and predictive analysis of field data.- Modeling of biofilm growth in porous media at the pore scale and up-scaling.- Coal tar contamination: Bioremediation and bioavailability.- The local discontinuous Galerkin method for advection-diffusion equations arising in groundwater and surface water applications.- Compaction and diagenesis.- Numerical simulation of freshwater, salt water and methane interaction processes in a coastal aquifer.- A preconditioning.
9 citations
03 Sep 2002
TL;DR: A new methodology based on mortar spaces which allow for multiple models and for dynamic upscaling not requiring pseudo functions is described and a new Discontinuous Galerkin discretization is introduced which is higher-order, locally conservative and allows for non-conforming grids.
Abstract: We address major computational science issues arising in modeling oil and gas production. We describe a new methodology based on mortar spaces which allow for multiple models and for dynamic upscaling not requiring pseudo functions. Also, we introduce a new Discontinuous Galerkin discretization which is higher-order, locally conservative and allows for non-conforming grids.