Journal ArticleJournal of Computational Physics · May 20, 2004
We apply second-order operator splitting to the Luo-Rudy I model for electrical wave propagation in the heart. The purpose of the operator splitting is to separate the nonlinear but local reaction computations from the linear but globally coupled diffusion ...
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Journal ArticleAdvances in Water Resources · August 1, 2002
Multi-component flow in porous media involves localized phenomena that could be due to several features, such as concentration fronts, wells or geometry of the media. Our approach to treating the localized phenomena is to use high-resolution discretization ...
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Journal ArticleAdvances in Water Resources · 1998
We review the current status of modeling multiphase systems, including balance equation formulation, constitutive relations for both pressure-saturation-conductivity and interphase mass transfer, and stochastic and computational issues. We discuss weakness ...
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Journal ArticleSIAM J. Sci. Comput. (USA) · 1998
We describe a numerical algorithm for the study of shear-band formation and growth in a 2D antiplane shear of granular materials. The algorithm combines front-tracking techniques and adaptive mesh refinement. Tracking provides a more careful evolution of t ...
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Journal ArticleJournal of Computational Physics · September 15, 1997
An adaptive local mesh refinement algorithm originally developed for unsteady gas dynamics by M. J. Berger is extended to incompressible flow in porous media. Multilevel iteration and domain decomposition methods are introduced to accommodate the elliptic/ ...
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Journal ArticleTransport in Porous Media · 1996
Previous pseudo-phase representations of micellar/polymer phase behavior have been highly successful in simulating enhanced oil recovery processes using conventional numerical methods. These models allowed for a variety of physical phenomena, such as the f ...
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Journal ArticleComputational Mechanics · 1994
The second-order Godunov method is extended to dynamic wave propagation in two-dimensional solids undergoing nonlinear finite deformation. It is shown that this explicit method is linearly stable for timesteps satisfying the standard CFL condition, does no ...
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Journal ArticleJournal of Computational Physics · January 1, 1992
In this paper the implementation of second-order Godunov methods for dynamic wave propagation in one-dimensional elastic-plastic solids is investigated. First, the Lagrangian form of the algorithm is reviewed, and then the algorithm is extended to the Eule ...
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Journal ArticleIMPACT of Computing in Science and Engineering · January 1, 1990
In this paper we describe a formally second-order algorithm for the dynamic response of one-dimensional soils and rock. There are two kinds of equations describing the motion of the material: the partial differential equations expressing conservation of mo ...
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Journal ArticleSociety of Petroleum Engineers of AIME, (Paper) SPE · 1987
A compositional reservoir simulator using a sequential formulation of the fluid flow and phase equilibrium equations requires that the phase equilibrium and associated derivatives of the dependent phase equilibrium variables with respect to the pressure an ...
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Journal ArticleChemical Engineering Science · January 1, 1987
This paper discusses a minimization algorithm for the solution of the Gibbs free energy minimization problem involving at most two phases. There are three major aspects to this paper. The first is the selection of descent directions and step lengths in ord ...
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Journal ArticleSociety of Petroleum Engineers of AIME, (Paper) SPE · 1985
This paper describes the formulation of vapor-liquid phase equilibrium as a linearly constrained minimization problem. It also describes a second minimization problem designed to test for local phase stability. Vectorized unconstrained minimization techniq ...
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Journal ArticleMath. Comput. (USA) · 1976
Considers Broyden's 1965 method for solving nonlinear equations. If the mapping is linear, then a simple modification of this method guarantees global and Q-superlinear convergence. For nonlinear mappings it is shown that the hybrid strategy for nonlinear ...
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